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eurus2_ground_truth_with_system

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AI2 Adapt Dev 46

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A teacher challenges her students with this new problem: Calculate the value of $\\left(7^2 - 5^2\\right)^3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $b_1$ , $b_2$ , $b_3$ , $c_1$ , $c_2$ , and $c_3$ be real numbers such that for every real number $x$ , we have\n\\[\n x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 = (x^2 + b_1 x + c_1)(x^2 + b_2 x + c_2)(x^2 + b_3 x + c_3). \n\\]\nCompute $b_1 c_1 + b_2 c_2 + b_3 c_3$ . \n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Point \\( M \\) divides side \\( BC \\) of triangle \\( ABC \\) in the ratio \\( BM: MC = 2:5 \\). Given that \\( \\overrightarrow{AB} = \\vec{a} \\) and \\( \\overrightarrow{AC} = \\vec{b} \\), find the vector \\( \\overrightarrow{AM} \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The largest decimal number that can be represented by a four-digit binary number.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the proposition \"$\\exists 0\\leqslant x\\leqslant 3$, $x^{2}-2x \\gt m$\" is a true proposition, then the range of $m$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The cost of three pencils and two pens is $\\$3.75$, and the cost of two pencils and three pens is $\\$4.05$. What is the cost of one pencil and one pen?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Determine the probability that two edges selected at random from the twelve edges of a cube with side length 1 are skew lines (i.e., non-intersecting and not in the same plane).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that $M$ is the least common multiple of all the integers $10$ through $30$, inclusive, and $N$ is the least common multiple of $M,32,33,34,35,36,37,38,39,$ and $40$, determine the value of $\\frac{N}{M}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $\\sin \\left(x- \\frac {\\pi}{4}\\right)= \\frac {3}{5}$, calculate the value of $\\cos \\left(x+ \\frac {\\pi}{4}\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "An interactive computer system has 20 terminals, each independently operated with a usage rate of 0.8 each. Calculate the probability that at least one of the 20 terminals is not in use.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "There are two kinds of containers: one weighing 130 kg and the other weighing 160 kg. How many containers of each kind are there if, together, they weigh 3 tons? Indicate all solutions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given an arithmetic sequence $\\{a_n\\}$ with a non-zero common difference $d$, some terms from $\\{a_n\\}$ form a geometric sequence, namely $a_{k_1}$, $a_{k_2}$, … $a_{k_n}$, where $k_1 = 1$, $k_2 = 5$, and $k_3 = 17$. Find: \n(1) The general term $k_n$; \n(2) The sum of the first n terms of the sequence $\\{k_n\\}$, denoted as $T_n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The measures of the interior angles of a convex pentagon form an increasing arithmetic sequence. How many such sequences are possible if the pentagon is not equiangular and all of the angle degree measures are positive integers less than 120 degrees?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $x^5 - x^4 + x^3 - px^2 + qx - 8$ is divisible by $(x + 2)(x - 2),$ find the ordered pair $(p,q).$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the equation of the line that passes through point A(1, 2) and is perpendicular to the line $2x + y - 5 = 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Vasya is furiously cutting a rectangular piece of paper with scissors. Every second he cuts the first piece he sees with a random straight cut into two parts.\n\na) Find the expected number of sides of the polygon that Vasya will randomly encounter after an hour of such work.\n\nb) Solve the same problem if the initial paper had the shape of an arbitrary polygon.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Masha wrote the number 547654765476 on a sheet of paper. She crossed out several digits so that the resulting number is the largest possible number divisible by 9. What is this number?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given a certain number of children rode past Zoe's house on scooters and quadricycles, and she counted 9 children and 30 wheels in total. How many quadricycles were there?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let U be the set of the 3000 smallest positive multiples of 5, and let V be the set of the 3000 smallest positive multiples of 7. Determine the number of elements common to U and V.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the greatest root of $f(x) = 21x^4 - 20x^2 + 3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Calculate $\\sqrt{\\frac{9}{49}+\\frac{16}{9}}$ and express it as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Triangle $PQR$ is a right triangle with legs $PQ$ and $PR$. Points $M$ and $N$ lie on legs $PQ$ and $PR$, respectively, so that $PM:MQ = PN:NQ = 1:3$. If $QN = 18$ units, and $MR = 30$ units, what is the length of hypotenuse $QR$? Express your answer in simplest radical form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given a sequence $\\{a_n\\}$ that satisfies $a_{p+q}=a_p+a_q$ for any $p,q \\in \\mathbb{N}^+$, and $a_2=-6$, calculate the value of $a_{11}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $0.75= \\frac{y}{210+x}$, find the smallest value of $x$, if $x$ and $y$ are positive integers.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In rectangle $LMNP$, points $Q$ and $R$ bisect $\\overline{LN}$, and points $S$ and $T$ bisect $\\overline{MP}$. Given that $LQ = QR = RS = ST = 1$ and $LN = MP = 4$, find the area of quadrilateral $WXYZ$ inside the rectangle formed by joining the midpoints of segments $\\overline{LQ}, \\overline{QR}, \\overline{RS}, \\overline{ST}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The seven digits in Lisa's phone number and the four digits in her zip code have the same sum. The four digits in her zip code are distinct, and her phone number is 465-3271. What is the largest possible value of Lisa's zip code?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "How many positive integers $n$ satisfy $400 < n^2 < 1600$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $60^{\\circ}$, and $| \\overrightarrow{a}|=1$, $|2 \\overrightarrow{a}- \\overrightarrow{b}|= \\sqrt {7}$, determine $| \\overrightarrow{b}|=$ \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The base 7 number $45x2_7$ is divisible by 9. What is the digit $x$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Mia plans to paint one wall in her living room. The wall is 10 feet high and 15 feet long. There is a 3-foot by 5-foot area on that wall that she will not have to paint due to a large painting hanging there. How many square feet will she need to paint?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The maximum and minimum values of the function y=4x-x^4 on the interval [-1, 2] are respectively found by evaluating the function at the critical points within the interval.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the integer values of \\( x \\) for which \\( x^{2} - 14x - 256 \\) is a perfect square.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the sum of the first six terms in the geometric sequence $\\frac14, \\frac1{16}, \\frac1{64}, \\dots$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "For \\(i=0,1, \\ldots, 5\\), let \\(l_{i}\\) be the ray on the Cartesian plane starting at the origin, at an angle \\(\\theta=i \\frac{\\pi}{3}\\) counterclockwise from the positive \\(x\\)-axis. For each \\(i\\), point \\(P_{i}\\) is chosen uniformly at random from the intersection of \\(l_{i}\\) with the unit disk. Consider the convex hull of the points \\(P_{i}\\), which will (with probability 1) be a convex polygon with \\(n\\) vertices for some \\(n\\). What is the expected value of \\(n\\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "How many of the integers between 1 and 2000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The perimeter of a rectangle is 30 meters. What is the number of square meters in the maximum possible area for this rectangle?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A coordinate system and parametric equations (4-4)\n\nGiven that the polar coordinate equation of circle $E$ is $ρ=4\\sin θ$, establish a planar rectangular coordinate system with the pole as the origin and the positive half of the polar axis as the $x$-axis, using the same unit length (where $(ρ,θ)$, $ρ≥0$, $θ∈[0,2π]$).\n1. Line $l$ passes through the origin with an inclination angle of $α=\\frac{3π}{4}$. Find the polar coordinates of the intersection point $A$ of line $l$ and circle $E$ (point $A$ is not the coordinate origin);\n2. Line $m$ passes through the midpoint $M$ of segment $OA$ and intersects circle $E$ at points $B$ and $C$. Find the maximum value of $||MB|-|MC||$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In $\\triangle ABC$, it is known that $|\\overrightarrow{AB}|=4, |\\overrightarrow{AC}|=1$, and the area of $\\triangle ABC$ is $\\sqrt{3}$. Find the value of $\\overrightarrow{AB} \\cdot \\overrightarrow{AC}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The cards in a stack of $2m$ cards are numbered consecutively from 1 through $2m$ from top to bottom. The top $m$ cards are removed, kept in order, and form pile $A$. The remaining cards form pile $B$. The cards are then restacked by taking cards alternately from the tops of pile $B$ and pile $A$, respectively. In this process, card number $(m+1)$ becomes the bottom card of the new stack, card number 1 is on top of this card, and so on, until piles $A$ and $B$ are exhausted. A stack is named magical if at least one card from each pile retains the same position it occupied in the original stack. Determine the number of cards in the magical stack in which card number 157 retains its original position.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A pair of vertices of a simple polygon is said to be \"visible\" to each other if and only if they are adjacent or the line segment connecting them lies entirely inside the polygon (excluding the endpoints on the boundary). Given a simple polygon with \\( n \\) vertices, where each vertex is exactly visible to four other vertices, find all possible values of the positive integer \\( n \\).\n\nNote: A simple polygon is a polygon without holes and does not intersect itself.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A cube with an edge length of $3$ inches is iced on all faces. It is cut into four vertical pieces as shown in a top view, where $N$ is a point one-third of the way along a top edge from a corner. The piece whose top is a trapezoid $C$ contains $c$ cubic inches of cake and $s$ square inches of icing. Calculate $c+s$.\nA) $30$\nB) $33$\nC) $36$\nD) $39$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $\\lg a+\\lg b=1$, then the minimum value of $a+2b$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In Mr. Thompson's class, $12$ of the $16$ students received a grade 'B' on their math test. If the same ratio of students received a 'B' in Mr. Jasper's class, and Mr. Jasper has $32$ students in total, how many students in Mr. Jasper's class received a 'B'?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the terminal side of angle $\\theta$ passes through the point $\\left(-\\frac{3}{5}, \\frac{4}{5}\\right)$, calculate the value of $\\sin\\left(\\frac{\\pi}{2}+\\theta\\right)+\\cos(\\pi-\\theta)+\\tan(2\\pi-\\theta)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In the seven-term sequence $P, Q, R, S, T, U, V$, the value of $S$ is $7$ and the sum of any three consecutive terms is $21$. What is $P+V$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "It is known that the relationship between the daily production cost $C$ (in yuan) and the production quantity $n$ (in pairs) of a certain shoe factory is $C = 4000 + 50n$.\n\n(1) Calculate the cost of producing 1000 pairs of shoes in one day; \n(2) If the production cost one day is 48,000 yuan, how many pairs of shoes were produced that day? \n(3) Assuming the selling price of each pair of shoes is 90 yuan, and all produced shoes are sold out, write the function relationship of the profit $P$ for that day with respect to the production quantity $n$ of that day, and calculate the minimum number of pairs of shoes that must be produced each day to avoid a loss?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "An infantry column stretched over 1 km. Sergeant Kim, riding a gyroscooter from the end of the column, reached its front and then returned to the end. During this time, the infantrymen covered 2 km 400 m. What distance did the sergeant travel during this time?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Factor the following expression: $75y + 45$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The number of sets $A$ satisfying $\\varnothing \\subsetneq A \\subseteq \\{1, 2, 3\\}$ is _________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Consider the $4\\times4$ array of $16$ dots, shown below.\n\n[asy]\nsize(2cm);\ndot((0,0));\ndot((1,0));\ndot((2,0));\ndot((3,0));\ndot((0,1));\ndot((1,1));\ndot((2,1));\ndot((3,1));\ndot((0,2));\ndot((1,2));\ndot((2,2));\ndot((3,2));\ndot((0,3));\ndot((1,3));\ndot((2,3));\ndot((3,3));\n[/asy]\n\nCounting the number of squares whose vertices are among the $16$ dots and whose sides are parallel to the sides of the grid, we find that there are nine $1\\times1$ squares, four $2\\times2$ squares, and one $3\\times3$ square, for a total of $14$ squares. We delete a number of these dots. What is the minimum number of dots that must be deleted so that each of the $14$ squares is missing at least one vertex?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $\\mathbb{F}_p$ be the set of integers modulo $p$ . Call a function $f : \\mathbb{F}_p^2 \\to \\mathbb{F}_p$ *quasiperiodic* if there exist $a,b \\in \\mathbb{F}_p$ , not both zero, so that $f(x + a, y + b) = f(x, y)$ for all $x,y \\in \\mathbb{F}_p$ .\nFind the number of functions $\\mathbb{F}_p^2 \\to \\mathbb{F}_p$ that can be written as the sum of some number of quasiperiodic functions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Geetha wants to cut a cube of size $4 \\times 4\\times 4$ into $64$ unit cubes (of size $1\\times 1\\times 1$ ). Every cut must be straight, and parallel to a face of the big cube. What\nis the minimum number of cuts that Geetha needs?\nNote: After every cut, she can rearrange the pieces before cutting again. At every\ncut, she can cut more than one pieces as long as the pieces are on a straight line.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "What is the largest positive integer $n$ for which $n^3 + 150$ is divisible by $n+5$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $a=2\\sqrt{2}$, $b=5$, and $c=\\sqrt{13}$. Find:\n\n$(Ⅰ)$ The measure of angle $C$;\n\n$(Ⅱ)$ The value of $\\sin A$;\n\n$(Ⅲ)$ The value of $\\sin \\left(2A+\\frac{\\pi}{4}\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If a parabola has its vertex at the origin and its directrix is $x = -1$, then the equation of this parabola is \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The average cost of a long-distance call in a specific country in 2000 was 15 cents per minute, and the average cost in 2020 increased to 25 cents per minute. Calculate the approximate percent increase in the cost per minute of a long-distance call.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $P(\\cos α, \\sin α)$ and $Q(\\cos β, \\sin β)$, calculate the maximum value of $|PQ|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $D$ be a point inside triangle $\\triangle ABC$ such that $AB = DC$, $\\angle DCA = 24^\\circ$, $\\angle DAC = 31^\\circ$, and $\\angle ABC = 55^\\circ$. Find $\\angle DAB$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "What is the remainder when $3^{2023}$ is divided by 5?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Define the sequence $S_n$ where $S_1 = 1$, $S_2 = 2$, and each subsequent term is the sum of the two preceding terms. Find the last digit of the 9th term in this sequence modulo 9.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A high school has a total of 900 students, among which there are 300 freshmen, 200 sophomores, and 400 juniors. Now, a stratified sampling method is used to draw a sample of 45 students. The number of students drawn from freshmen, sophomores, and juniors respectively is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A nine-digit number 222222222 is written on a blackboard. The following operation is performed on this number: erase the last digit, multiply the remaining number by 4, then add the erased digit back to the result, and write the number on the blackboard. This process is repeated until a single digit number is obtained. What is this single digit number?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the function $f(x)=\\sin (\\omega x+\\varphi)$ ($\\omega > 0$, $|\\varphi| \\leqslant \\frac{\\pi}{2}$), $x=-\\frac{\\pi}{4}$ is a zero of $f(x)$, $x=\\frac{\\pi}{4}$ is the axis of symmetry for the graph of $y=f(x)$, and $f(x)$ is monotonic on the interval $\\left(\\frac{\\pi}{18},\\frac{5\\pi}{36}\\right)$, calculate the maximum value of $\\omega$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "For each integer $n$ greater than 1, let $G(n)$ be the number of solutions of the equation $\\cos x = \\cos nx$ on the interval $[0, \\pi]$. What is $\\sum_{n=2}^{2007} G(n)$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $0 \\le p \\le 1$ and $0 \\le q \\le 1$, define $H(p, q)$ by\n\\[\n H(p, q) = -3pq + 4p(1-q) + 4(1-p)q - 5(1-p)(1-q).\n\\]\nDefine $J(p)$ to be the maximum of $H(p, q)$ over all $q$ (in the interval $0 \\le q \\le 1$). What is the value of $p$ (in the interval $0 \\le p \\le 1$) that minimizes $J(p)$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The hyperbola has its two foci at (-6,0) and (6,0), and passes through the point (-5,2). Determine the standard equation of the hyperbola.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A sequence is defined as an \"equal sum sequence\" if the sum of each term and its subsequent term is a constant. This constant is referred to as the public sum of the sequence. Given that sequence $\\{a\\_n\\}$ is an equal sum sequence, with $a\\_1=2$ and a public sum of $5$, find the value of $a\\_{18}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The equation $\\left(x-1\\right)\\left(2x+1\\right)=2$ in general form is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the sets A={x|x^2^-4x-5≤0}, B={x|1<2^x<4}, and C={x|x<m}.\n(1) Find A∩(∁\\_RB);\n(2) If A∩C≠A and B∩C≠∅, find the range of real number m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the power function $f(x)=x^{(2-k)(1+k)}$, where $k \\in \\mathbb{Z}$, and $f(x)$ is monotonically increasing on $(0,+\\infty)$.\n(1) Find the value of the real number $k$ and write out the corresponding function expression of $f(x)$;\n(2) If $F(x) = 2f(x) - 4x + 3$ is not monotonic on the interval $[2a, a + 1]$, find the range of values of the real number $a$;\n(3) Determine whether there exists a positive number $q$ such that the function $g(x) = 1 - qf(x) + (2q - 1)x$ has a range of $[-4, \\frac{17}{8}]$ on the interval $[-1, 2]$. If it exists, find the value of $q$; if not, explain the reason.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The foot of the perpendicular from the origin to a plane is \\((10, -2, 5)\\). Find the equation of the plane. Enter your answer in the form\n\\[Ax + By + Cz + D = 0,\\]\nwhere \\(A,\\) \\(B,\\) \\(C,\\) \\(D\\) are integers such that \\(A > 0\\) and \\(\\gcd(|A|,|B|,|C|,|D|) = 1.\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "\nA chess piece can move 8 or 9 squares horizontally or vertically. It is forbidden to move onto the same square twice.\n\nWhat is the maximum number of squares this piece can cover on a $15 \\times 15$ board? (The tour can start from any square.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Xiaomin and Xiaoxia, two students, solved the equation $3\\left(x-3\\right)=\\left(x-3\\right)^{2}$ as shown in the following table:<br/>\n\n| Xiaomin | Xiaoxia |\n|---------|---------|\n| Divide both sides by $\\left(x-3\\right)$, we get $3=x-3$, hence $x=6$. | Moving terms, we get $3\\left(x-3\\right)-\\left(x-3\\right)^{2}=0$, extracting common factors, we get $\\left(x-3\\right)\\left(3-x-3\\right)=0$. Therefore, $x-3=0$ or $3-x-3=0$, which gives $x_{1}=3$, $x_{2}=0$. |\n\n$(1)$ Do you think their solutions are correct? If correct, mark with \"$\\surd $\"; if incorrect, mark with \"$\\times $\": Xiaomin______, Xiaoxia______;<br/>$(2)$ Write down your solution process.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Simplify: $\\frac{3 \\cdot 2^{n+5} - 5 \\cdot 2^n}{4 \\cdot 2^{n+2}}$. Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The number 340! ends in how many zeros when expressed as an integer?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given a circle $C: x^{2}+y^{2}=4$ and a line $l: y=kx+m$, determine the possible values of $m$ when the minimum chord length, resulting from varying the value of $k$, is equal to $2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given points $F_{1}$ and $F_{2}$ are the common foci of the ellipse $C_{1}: \\dfrac {x^{2}}{a^{2}}+ \\dfrac {y^{2}}{b^{2}}=1$ (with $a > b > 0$) and the hyperbola $C_2: \\dfrac {x^{2}}{a'^{2}}- \\dfrac {y^{2}}{b'^{2}}=1$ (with $a' > 0, b' > 0$), point $P$ is an intersection point of the two curves and satisfies $\\angle F_{1}PF_{2}=90^{\\circ}$. Let the eccentricities of the ellipse and hyperbola be $e_{1}$ and $e_{2}$ respectively, then find the value of $\\dfrac {1}{e_{1}^{2}}+ \\dfrac {1}{e_{2}^{2}}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A pyramid $PQRS$ has a rectangular base $QRS$ with $QR = 10$, $RS = 5$. If $\\overline{PQ}\\perp \\overline{QR}$, $\\overline{PQ}\\perp \\overline{QS}$, and $PQ = 9$, find the volume of pyramid $PQRS$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The sides of the convex quadrilateral ABCD are AB = 3, BC = 4, CD = 12, and DA = 13. The angle ∠CBA is a right angle. Determine the area of the quadrilateral.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $\\overrightarrow{a} = (-2, 1)$, $|\\overrightarrow{b}| = 5$, and $\\overrightarrow{a} \\parallel \\overrightarrow{b}$, find $\\overrightarrow{b}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the coefficient of the $x^{2}$ term in the expansion of $((1-x)^{3}(2x^{2}+1)^{5})$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Regular octagon $ABCDE$ and regular decagon $AEFGHIJKLM$ are drawn on opposite sides of line segment $AE$ such that they are coplanar. What is the degree measure of exterior angle $DEF$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The lines $x = \\frac{1}{3}y + a$ and $y = \\frac{1}{3}x + b$ intersect at the point $(3,4)$. What is $a + b$?\nA) $\\frac{11}{3}$ \nB) $\\frac{12}{3}$ \nC) $\\frac{13}{3}$ \nD) $\\frac{14}{3}$ \nE) $\\frac{15}{3}$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A two-digit number, when multiplied by 109, yields a four-digit number. It is divisible by 23, and the quotient is a one-digit number. The maximum value of this two-digit number is $\\qquad$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In the Cartesian coordinate system $xOy$, the right directrix of the hyperbola $\\frac{x^2}{3} - y^2 = 1$ intersects its two asymptotes at points $P$ and $Q$, and its foci are $F_1$ and $F_2$. The area of the quadrilateral $F_1PF_2Q$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $m+1$ is the opposite number of $-4$, then the value of $m$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are real numbers satisfying:\n\\[\na+b+c = -4,\n\\]\n\\[\na+b+d = 2,\n\\]\n\\[\na+c+d = 15,\n\\]\n\\[\nb+c+d = 10,\n\\]\nwhat is \\(ab + cd\\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The function \\( f(x) = a^{2x} + 3a^x - 2 \\) (where \\( a > 0 \\) and \\( a \\neq 1 \\)) has a maximum value of 8 on the interval \\( x \\in [-1, 1] \\). Determine its minimum value on this interval.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Xiaogang and Xiaoqiang set off from two places $A$ and $B$ at the same time. Xiaogang rides a bicycle, while Xiaoqiang walks, moving towards each other at a constant speed along the same route. They meet after $2$ hours, with Xiaogang having traveled $24$ km more than Xiaoqiang when they meet. After meeting, Xiaogang arrives at place $B$ after $0.5$ hours. What are the speeds of Xiaogang and Xiaoqiang respectively? How long does it take for Xiaoqiang to arrive at place $A$ after they meet?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that $f(x)$ is an odd function defined on $\\mathbb{R}$ and satisfies $f(x+4) = f(x)$, and $f(x) = 2x^2$ when $x \\in (0, 2)$, find the value of $f(7)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Determine how many triangles can be formed using the vertices of a regular hexadecagon (a 16-sided polygon).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given an ellipse $\\frac{{x}^{2}}{{a}^{2}}+\\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$ with the left focus $F$ and eccentricity $\\frac{\\sqrt{3}}{3}$, a line $l$ passing through $F$ intersects the ellipse at points $A$ and $B$, where $|AF|=3|FB|$. The slope of line $l$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $n$ be a positive integer. An $n\\times n$ board consisting of $n^2$ cells, each being a unit square colored either black or white, is called *convex* if for every black colored cell, both the cell directly to the left of it and the cell directly above it are also colored black. We define the *beauty* of a board as the number of pairs of its cells $(u,v)$ such that $u$ is black, $v$ is white, and $u$ and $v$ are in the same row or column. Determine the maximum possible beauty of a convex $n\\times n$ board.\n\n*Proposed by Ivan Novak*\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Proposition $q: \\forall x \\in \\mathbb{R}$, $ax^{2}+4x+a \\geq -2x^{2}+1$. If proposition $q$ is false, find the range of real number $a$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The solution set of the inequality $ax^2+bx+c<0$ is $\\{x|x<-2 \\text{ or } x>-\\frac{1}{2}\\}$. Find the solution set of the inequality $ax^2-bx+c>0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "On a spherical planet with diameter $10,000 \\mathrm{~km}$, powerful explosives are placed at the north and south poles. The explosives are designed to vaporize all matter within $5,000 \\mathrm{~km}$ of ground zero and leave anything beyond $5,000 \\mathrm{~km}$ untouched. After the explosives are set off, what is the new surface area of the planet, in square kilometers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A line whose $y$-intercept is $(0,3)$ intersects the ellipse $4x^2 + 9y^2 = 36.$ Find all possible slopes of this line.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In a company, several employees earn a total monthly salary of $10,000. A kind manager proposes to triple the salaries of those earning up to $500 and increase the salaries of the others by $1,000, making the total salary $24,000. An unkind manager proposes to reduce the salaries of those earning more than $500 to $500, while keeping the others' salaries unchanged. What will the total salary be in this case?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "There are 6 students standing in a row, and students A and B cannot stand together. How many different arrangements are there?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]