messages
listlengths 3
3
| ground_truth
stringlengths 1
2.25k
| dataset
stringclasses 1
value |
|---|---|---|
[
{
"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 sequence $\\{a_n\\}$ is an arithmetic sequence, satisfying $$\\overrightarrow {OA} = a_{3} \\overrightarrow {AB} + a_{2016} \\overrightarrow {AC}$$, where A, B, C are on the same line, and O is a point outside line AB. Denote the sum of the first n terms of the sequence $\\{a_n\\}$ as $S_n$, then calculate the value of $S_{2018}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac {2018}{2} | MATH |
[
{
"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 square \\(ABCD\\) with a side length of 10, points \\(P\\) and \\(Q\\) lie on the segment joining the midpoints of sides \\(AD\\) and \\(BC\\). Connecting \\(PA\\), \\(PC\\), \\(QA\\), and \\(QC\\) divides the square into three regions of equal area. Find the length of segment \\(PQ\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{20}{3} | MATH |
[
{
"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 intersection points between the graph of the quadratic function $f(x) = ax^2 + bx + c$ and the x-axis is equal to the number of real solutions of the equation $ax^2 + bx + c = 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 0 | MATH |
[
{
"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": "Compute $2\\log _{3}2-\\log _{3} \\dfrac {32}{9}+\\log _{3}8-5^{\\log _{5}3}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -1 | MATH |
[
{
"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 how many positive integer values of $N$ does the expression $\\dfrac{48}{N+3}$ result in an integer?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 7 | MATH |
[
{
"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 $f(x)=(x+1)\\ln x-a(x-1)$.\n\n (Ⅰ) When $a=4$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$;\n\n (Ⅱ) When $x\\in (1,+\\infty)$, it always holds that $f(x) > 0$, find the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (-\infty,2] | MATH |
[
{
"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": "You have five shirts, four pairs of pants, and two hats. How many different outfits consisting of one shirt, one pair of pants, and one hat can you make?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 40 | MATH |
[
{
"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 $f(x) = -x^3 + x^2 + tx + t$ is increasing on the interval $(-1, 1)$. Determine the range of values for $t$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | t \geq 5 | MATH |
[
{
"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 class of 42 students, 3 students did not achieve the required credits in the compulsory mathematics 1 credit exam. The probability of the event \"participating in a makeup exam\" is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{1}{14} | MATH |
[
{
"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 5 chairs in a row for 3 people to sit on. It is required that persons A and B must sit next to each other, and the three people cannot all sit next to each other. How many different seating arrangements are there?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 12 | MATH |
[
{
"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 goat eats 1 cartload of hay in 6 weeks, a sheep in 8 weeks, and a cow in 3 weeks. How many weeks will it take for 5 goats, 3 sheep, and 2 cows together to eat 30 cartloads of hay?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 16 | MATH |
[
{
"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 $f(x)$ is defined for all integers $x \\ge 0,$ $f(1) = 2,$ and\n\\[f(a + b) = f(a) + f(b) - 2f(a \\cdot b)\\]for all integers $a,$ $b \\ge 0,$ compute $f(1986).$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 box contains 7 chips, numbered 1, 2, 3, 4, 5, 6, and 7. Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds 9. Calculate the probability that 3 draws are required and the last chip drawn is an odd number.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{1}{14} | MATH |
[
{
"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 circle with a radius of 3 units has its center at $(0, 0)$. A circle with a radius of 8 units has its center at $(17, 0)$. A line tangent to both circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. What is the value of $x$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{51}{11} | MATH |
[
{
"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 degree measure of an interior angle of a regular hexagon?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 120\text{ degrees} | MATH |
[
{
"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 point $P$ is on the line $l: \\sqrt {3}x-y+2=0$, and point $Q$ is on the circle $C: x^{2}+y^{2}+2y=0$, find the minimum distance between points $P$ and $Q$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{1}{2} | MATH |
[
{
"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": "Solve the equation: $1- \\frac {1}{x-1}= \\frac {2x}{1-x}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{2}{3} | MATH |
[
{
"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": "Suppose there is an infinite sequence of lights numbered \\(1,2,3, \\ldots\\), and you know the following two rules about how the lights work:\n- If the light numbered \\(k\\) is on, the lights numbered \\(2k\\) and \\(2k+1\\) are also guaranteed to be on.\n- If the light numbered \\(k\\) is off, then the lights numbered \\(4k+1\\) and \\(4k+3\\) are also guaranteed to be off.\nSuppose you notice that light number 2023 is on. Identify all the lights that are guaranteed to be on?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \text{All lights numbered } 1, 2, 3, \ldots \text{ are on} | MATH |
[
{
"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 geometric sequence \\{a_n\\}, given that a_2 = 8 and a_5 = 64, find the common ratio \\(q\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 \\(abc = 1\\), \\(a + b + c = 2\\), and \\(a^2 + b^2 + c^2 = 3\\), find the value of \\(\\frac{1}{ab + c - 1} + \\frac{1}{bc + a - 1} + \\frac{1}{ca + b - 1}\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -\frac{2}{3} | MATH |
[
{
"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": "Completely factor the following expression: $16y^3 + 8y^2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 8y^2(2y + 1) | MATH |
[
{
"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 $f\\left(x\\right)=x^{2}-ax+4$. \n$(1)$ When $a=3$, find the range of $f\\left(x\\right)$ on the interval $\\left[1,3\\right]$. \n$(2)$ If the maximum value of $f\\left(x\\right)$ on the interval $\\left[0,2\\right]$ is $4$, find the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | [2, +\infty) | MATH |
[
{
"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": "Among the following statements, the correct propositions are \\_\\_\\_\\_\\_\\_ ; (Fill in the numbers of all correct propositions) \n① If line $l$ is parallel to plane $\\alpha$, and line $l$ is parallel to plane $\\beta$, then $\\alpha$ is parallel to $\\beta$, \n② If line $l$ is perpendicular to plane $\\alpha$, and line $l$ is perpendicular to plane $\\beta$, then $\\alpha$ is parallel to $\\beta$, \n③ If two lines $l_1$ and $l_2$ form equal angles with plane $\\alpha$, then $l_1$ is parallel to $l_2$, \n④ If two different points $A$ and $B$ on line $l$ are at equal distances from plane $\\alpha$, then $l$ is parallel to $\\alpha$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | ② | MATH |
[
{
"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 even divisors does $8!$ have?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 84 | MATH |
[
{
"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 \\(\\sin \\left( \\frac{3\\pi}{2} \\right).\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -1 | MATH |
[
{
"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 bookstore marks down the price of a book originally priced at $\\$20$. The price is first reduced by $25\\%$. After this initial markdown, the reduced price is further lowered by $40\\%$. What is the final price of the book, in dollars?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \$9 | MATH |
[
{
"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 distance from the point \\( M_{0} \\) to the plane passing through three points \\( M_{1}, M_{2}, M_{3} \\).\n\n\\( M_{1}(7, 2, 4) \\)\n\n\\( M_{2}(7, -1, -2) \\)\n\n\\( M_{3}(-5, -2, -1) \\)\n\n\\( M_{0}(10, 1, 8) \\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 3 | MATH |
[
{
"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 sequence $\\{a_n\\}$ is a geometric sequence with a common ratio greater than 1, and the sum of its first $n$ terms is $S_n$. If $a_1$ and $a_3$ are the roots of the equation $x^2-5x+4=0$, then $S_3=$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 7 | MATH |
[
{
"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": "\nWhat is the largest integer \\( n \\) which cannot be represented as \\( 8a + 15b \\) with \\( a \\) and \\( b \\) non-negative integers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 97 | MATH |
[
{
"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 a student's Chinese score (x) is higher than 85 points and their Mathematics score (y) is not less than 80 points, determine the system of inequalities that represents this situation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \begin{cases}
x > 85 \\
y \geq 80
\end{cases} | MATH |
[
{
"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 sum of the coefficients of all terms in the expansion of $(1+x+ax^{3})(x+ \\frac{1}{x})^{5}$ is $96$, find the constant term of this expansion.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 15 | MATH |
[
{
"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 remainders when three positive integers are divided by 7 are 2, 3, and 5. Find the remainder when their product is divided by 7.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 $t\\in \\mathbb{R}$, vector $\\overrightarrow{a}=(2,1)$, $\\overrightarrow{b}=(4,t)$. If $\\overrightarrow{a}$ is parallel to $\\overrightarrow{b}$, then $t=\\_\\_\\_\\_\\_\\_$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 surface area of a cube is thrice that of a cube with volume 8 cubic units, find the side length of this larger cube.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2\sqrt{3} | MATH |
[
{
"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 the area of the region defined by the equation $x^2 + y^2 + 6x - 8y + 9 = 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 16\pi | MATH |
[
{
"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 value of the definite integral $\\int_{-1}^{1} [\\sqrt{1-x^2} + \\cos(2x - \\frac{\\pi}{2})] dx$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{\pi}{2} | MATH |
[
{
"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": "6. Three targets. A shooter fires at three targets until all are hit. The probability of hitting a target with a single shot is \\( p \\). \n\na) Find the probability that exactly 5 shots are needed.\n\nb) Find the expected number of shots needed.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{3}{p} | MATH |
[
{
"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 roots of $64x^3-144x^2+92x-15=0$ are in arithmetic progression. Find the difference between the largest and smallest roots.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1 | MATH |
[
{
"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 $\\#N$ by the formula $\\#N = (.5N)^2 + 1$. Calculate $\\#(\\#(\\#20))$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1627102.64 | MATH |
[
{
"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 prime factor of $4752$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 11 | MATH |
[
{
"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 line $l$ passing through point $P(1, -2)$ intersects the circle $C: (x-2)^2+(y+3)^2=9$ at points $A$ and $B$. Find the equation of the line $l$ when $\\angle ACB$ is minimized.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | x-y-3=0 | MATH |
[
{
"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 $$f(x)=A\\sin(3x+ \\frac {\\pi}{6})+B(A>0)$$ has a maximum value of 2 and a minimum value of 0. \n(1) Find the value of $$f( \\frac {7\\pi}{18})$$; \n(2) After translating the graph of the function $$y=f(x)$$ to the right by $$\\frac {\\pi}{6}$$ units, and then enlarging the y-coordinates of all points on the graph by a factor of $$\\sqrt {2}$$ (while keeping the x-coordinates unchanged) to obtain the graph of the function $$y=g(x)$$, find the solution to the equation $$g(x)= \\frac { \\sqrt {2}}{2}$$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \{x|x= \frac {2}{3}k\pi+ \frac {\pi}{2}, \text{ or } x= \frac {2}{3}k\pi+ \frac {13\pi}{18}, k\in\mathbb{Z}\} | MATH |
[
{
"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 $x-1 \\gt 0$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | x \gt 1 | MATH |
[
{
"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 area of the triangle formed by the tangent line to the curve $y=x$ at the point $(a,a^{2}) (a > 0)$ and the two coordinate axes is $2$, find the value of the real number $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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": "Construct a new shape by adding an eighth unit cube to the previously described configuration of seven cubes. Place this new cube adjacent to one of the six outlying cubes from the central cube. What is the ratio of the volume in cubic units to the surface area in square units for this new configuration?\nA) $\\frac{8}{31}$\nB) $\\frac{8}{32}$\nC) $\\frac{8}{33}$\nD) $\\frac{8}{34}$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{8}{33} | MATH |
[
{
"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 function $f(x), x \\in R$ satisfies $f(1)=1$, and ${f}{{'}}(x) < 1$, determine the solution set for the inequality $f(\\lg ^{2}(x)) < \\lg ^{2}(x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (\frac{1}{10}, 10) | MATH |
[
{
"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 $\\mathbf{Q}$ be the matrix for projecting onto the vector $\\begin{pmatrix} 3 \\\\\\ 5 \\end{pmatrix}.$ Find $\\det \\mathbf{Q}.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 0 | MATH |
[
{
"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 parallelogram $EFGH$, angle $E$ measures $135^\\circ$. Find the measure of angle $G$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 135^\circ | MATH |
[
{
"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 $f(x)=x^{5}-3x^{3}-6x^{2}+x-1$, calculate the value of $f(-2)$ using the Horner's method.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -39 | MATH |
[
{
"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": "Mr. Wang went to the city administrative center building for business. Assuming that going up one floor is recorded as +1, and going down one floor is recorded as -1, Mr. Wang started from the 1st floor, and the sequence of the elevator moving up and down floors is as follows (unit: floor): +6, -3, +10, -8, +12, -7, -10. \n(1) Please calculate to explain whether Mr. Wang finally returned to the starting point on the 1st floor. \n(2) Each floor of the center building is 3m high, and the elevator consumes 0.2 kWh of electricity for every 1m it moves up or down. Based on Mr. Wang's current location, please calculate how much electricity the elevator consumed during his visit?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 33.6 | MATH |
[
{
"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 $\\triangle ABC$, $AB = 18$, $BC = 14$ and $CA = 15$. Point $M$ is on side $AB$ such that $AM = 3$ and $MB = 15$. Point $H$ is the foot of the altitude from $A$ to $BC$. Calculate the length of $HM$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \sqrt{291} | MATH |
[
{
"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": "Convert $253_{10}$ to base 2. Let $a$ be the number of zeros and $b$ be the number of ones in base 2. What is the value of $b-a?$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 6 | MATH |
[
{
"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": "Express 106,000 in scientific notation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1.06 \times 10^{5} | MATH |
[
{
"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:<br/>$(1)-20+\\left(-14\\right)-\\left(-18\\right)-13$;<br/>$(2)-24×(-\\frac{1}{2}+\\frac{3}{4}-\\frac{1}{3})$;<br/>$(3)-49\\frac{24}{25}\\times 10$ (simplified calculation);<br/>$(4)-{3}^{2}+[(-\\frac{1}{3})×(-3)-\\frac{8}{5}÷{2}^{2}]$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -8\frac{2}{5} | MATH |
[
{
"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 number halfway between $\\dfrac{1}{8}$ and $\\dfrac{1}{3}$.\nA) $\\dfrac{11}{48}$\nB) $\\dfrac{11}{24}$\nC) $\\dfrac{1}{2}$\nD) $\\dfrac{7}{24}$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \text{A) } \frac{11}{48} | MATH |
[
{
"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 earthquake occurred in a certain area, and $550$ tents are needed to solve the temporary accommodation problem for the disaster-affected people. Now two factories, A and B, are processing and producing the tents. It is known that the daily processing capacity of factory A is $1.5$ times that of factory B, and factory A takes $4$ days less than factory B to process and produce $240$ tents.\n\n$(1)$ Find out how many tents each factory can process and produce per day.\n\n$(2)$ If the daily processing cost of factory A is $30,000$ yuan and the daily processing cost of factory B is $24,000$ yuan, in order to ensure that the total processing cost of these disaster relief tents does not exceed $600,000$ yuan, how many days should factory A be arranged to process and produce at least?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \text{At least 10 days} | MATH |
[
{
"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 equations \n\\[90x^4 + ax^3 + bx^2 + cx + 16 = 0\\] \nand \n\\[16x^5 + dx^4 + ex^3 + fx^2 + gx + 90 = 0\\]\nthat have a common rational root $k$, which is not an integer and is negative. Identify $k$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -\frac{1}{2} | MATH |
[
{
"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": "Seven students are standing in a row for a graduation photo. Among them, student A must stand in the middle, and students B and C must 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"
}
] | 192 | MATH |
[
{
"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 ways are there to divide a group of 8 friends among the basketball team, the soccer team, the track team, and the volleyball team? (Each team could have anywhere from 0 to 8 of the friends on it. Assume the friends are distinguishable.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 65536 | MATH |
[
{
"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 \\(\\sin \\frac{13 \\pi}{4}.\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -\frac{\sqrt{2}}{2} | MATH |
[
{
"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 \\(\\left\\{a_{n}\\right\\}\\) be a sequence such that \\(a_{1}=20\\), \\(a_{2}=17\\) and \\(a_{n}+2a_{n-2}=3a_{n-1}\\). Determine the value of \\(a_{2017} - a_{2016}\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -3 \cdot 2^{2015} | MATH |
[
{
"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": "1 jin of oranges and 2 jin of pears together cost 8.9 yuan, 2 jin of apples and 3 jin of pears together cost 23 yuan, 3 jin of apples and 4 jin of oranges together cost 30.1 yuan. What is the cost per jin of oranges, pears, and apples?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2.5, 3.2, 6.7 | MATH |
[
{
"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 $S$ be the set of all polynomials $Q(x,y,z)$ with coefficients in $\\{0,1\\}$ such that there exists a homogeneous polynomial $P(x,y,z)$ of degree $2016$ with integer coefficients and a polynomial $R(x,y,z)$ with integer coefficients so that \\[P(x,y,z) Q(x,y,z) = P(yz,zx,xy)+2R(x,y,z)\\] and $P(1,1,1)$ is odd. Determine the size of $S$ .\n\nNote: A homogeneous polynomial of degree $d$ consists solely of terms of degree $d$ .\n\n*Proposed by Vincent Huang*\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 509545 | MATH |
[
{
"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 $f\\left(x\\right)$ is an even function on $R$, when $x\\geqslant 0$, $f\\left(x\\right)=e^{x-2}-2e$. \n$(1)$ When $x \\lt 0$, find the analytical expression of $f\\left(x\\right)$; \n$(2)$ If $f\\left(a\\right)+f\\left(3\\right) \\lt 0$, find the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (-3 - \ln 3, 3 + \ln 3) | MATH |
[
{
"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 $f(x)$ be a function with domain $[0,3]$ and range $[0,2]$, described by \\( f(x) = \\frac{x^2}{3} \\). Define a new function $g(x)$ by:\n\\[ g(x) = 2 - f(x^2 + 1) \\]\nDetermine the domain and range of $g(x)$, and provide the ordered quadruple $(a, b, c, d)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (-\sqrt{2}, \sqrt{2}, -1, \frac{5}{3}) | MATH |
[
{
"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": "\nOn a coordinate plane, a square \\( K \\) is marked with vertices at points \\((0,0)\\) and \\((10,10)\\). Inside this square, depict the set \\( M \\) of points \\((x, y)\\) whose coordinates satisfy the equation\n\n\\[ [x] = [y], \\]\n\nwhere \\([a]\\) denotes the integer part of number \\(a\\) (that is, the largest integer not exceeding \\(a\\); for example, \\([10]=10, [9.93]=9, [1 / 9]=0, [-1.7]=-2\\)). What part of the area of square \\( K \\) does the area of set \\( M \\) constitute?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 10\% | MATH |
[
{
"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": "Line $l_1$ has the equation $4x - 3y = 2$ and passes through $A = (0, -2)$. Line $l_2$ has the equation $y = 2$ and intersects line $l_1$ at point $B$. Line $l_3$ has positive slope, goes through point $A$, and intersects $l_2$ at point $C$. The area of $\\triangle ABC$ is $6$. Find the slope of $l_3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{4}{5} | MATH |
[
{
"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 \\( f(x) = 3\\sqrt{x} + \\frac{18}{\\sqrt{x}} \\) and let \\( g(x) = 3x^2 - 3x - 4 \\). What is \\( f(g(4)) \\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 14.25\sqrt{2} | MATH |
[
{
"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 eccentricity of the hyperbola $\\frac {x^{2}}{a^{2}}- \\frac {y^{2}}{3}=1$ is 2, calculate the distance from the vertex of the hyperbola to the asymptote.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac {\sqrt {3}}{2} | MATH |
[
{
"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 unit square is cut into four pieces that can be arranged to make an isosceles triangle as shown below. What is the perimeter of the triangle? Express your answer in simplest radical form.\n\n[asy]\nfilldraw((0, 3)--(-1, 3)--(-2, 2)--(-1, 1)--cycle,lightgrey);\nfilldraw((0, 3)--(1, 3)--(2, 2)--(1, 1)--cycle,lightgrey);\nfilldraw((0, 4)--(-1, 3)--(1, 3)--cycle,grey);\ndraw((-1, 1)--(0,0)--(1, 1));\n\nfilldraw((4,1)--(3,2)--(2,0)--(3,0)--cycle,lightgrey);\nfilldraw((4,1)--(5,2)--(6,0)--(5,0)--cycle,lightgrey);\nfilldraw((4,1)--(3,0)--(5,0)--cycle,grey);\ndraw((3,2)--(4,4)--(5,2));\n[/asy]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2\sqrt{2} | MATH |
[
{
"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 integer part of the value of \\( 28.816 \\div (0.40 + 0.41 + 0.42 + \\cdots + 0.59) \\) can be determined.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 all values of $x$ such that $2^{x^2-5x-4} = 8^{x-5}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 12 | MATH |
[
{
"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 rows of Pascal's Triangle contain the number $53$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1 | MATH |
[
{
"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 natural number \\(A\\), written in the decimal system, is obtained from a number \\(B\\) by moving its last digit to the first position. It is known that the number \\(B\\) is coprime with the number 24 and \\(B > 666666666\\). Find the largest and smallest numbers \\(A\\) that satisfy these conditions. (Two natural numbers are coprime if they have no common divisors other than one).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 999999998 | MATH |
[
{
"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 angle $\\alpha$ is in the second quadrant and $\\cos\\left( \\frac{\\pi}{2} - \\alpha \\right) = \\frac{4}{5}$, then $\\cos\\alpha =$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \cos\alpha = -\frac{3}{5} | MATH |
[
{
"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": "Two equilateral triangles \\( CEF \\) and \\( DIH \\) are positioned as shown in the diagram. The measures of some angles are marked in the diagram. Find the measure of angle \\( x \\). Give the answer in degrees.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 40^\circ | MATH |
[
{
"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 line symmetric to $3x-4y+5=0$ with respect to the y-axis is _______________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 3x+4y+22=0 | MATH |
[
{
"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 geometric sequence where the common ratio is greater than 1, what is the maximum number of terms that are integers between 100 and 1000?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 6 | MATH |
[
{
"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 degree measures of the angles of nondegenerate hexagon $ABCDEF$ are integers that form a non-constant arithmetic sequence in some order, and $\\angle A$ is the smallest angle of the (not necessarily convex) hexagon. Compute the sum of all possible degree measures of $\\angle A$ .\n\n*Proposed by Lewis Chen*\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1500^\circ | MATH |
[
{
"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 $a,$ $b,$ $c$ be positive real numbers such that $a + b + c = 3.$ Find the minimum value of\n\\[\n\\frac{1}{2a + b} + \\frac{1}{2b + c} + \\frac{1}{2c + a}.\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 3 | MATH |
[
{
"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 computer can perform 12,000 additions per second and twice as many multiplications per second. How many operations in total can it perform in three hours?\nA) 360,000,000\nB) 380,800,000\nC) 388,800,000\nD) 390,000,000\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | C) 388,800,000 | MATH |
[
{
"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 $f(x) = x^n + 1$ always passes through a fixed point. What are the coordinates of this fixed point?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (1, 2) | MATH |
[
{
"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 $\\{a_n\\}$, the sum of the first $n$ terms is $S_n$, and it satisfies $a_2+a_7+a_8+a_{11}=48$, $a_3:a_{11}=1:2$. Find $$\\lim_{n\\rightarrow \\infty } \\frac {na_{n}}{S_{2n}}$$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac {1}{2} | MATH |
[
{
"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 the complex number $z=\\frac{3+i}{1-2i}$ (where $i$ is the imaginary unit), find $|\\overline{z}|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \sqrt{2} | MATH |
[
{
"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, $\\triangle ABC$ has $\\angle BAC = \\angle BCA$. Given $BC=8$ and $AB=13$, what is the perimeter of $\\triangle ABC$?\n```plaintext\ndraw((0,0)--(6,10.39)--(12,0)--cycle);\nlabel(\"8\",(6,0),S);\nlabel(\"$B$\",(0,0),SW);\nlabel(\"$C$\",(12,0),SE);\nlabel(\"$A$\",(6,10.39),N);\nlabel(\"13\",(9,5.2));\n```\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 34 | MATH |
[
{
"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": "Circle $C_{1}$: $x^{2}+y^{2}+2x+2y-2=0$ and circle $C_{2}$: $x^{2}+y^{2}-4x-2y+1=0$ find the number of lines that are common to these two circles.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 | MATH |
[
{
"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 $\\{a_n\\}$, where $a_3=4$ and $a_2+a_6=10$. \n$(1)$ Find the general formula for $\\{a_n\\}$. \n$(2)$ Find the sum of the first $n$ terms of $\\left\\{ \\frac{a_n}{2^n} \\right\\}$, denoted as $T_n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | T_n=3- \frac{n+3}{2^n} | MATH |
[
{
"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 approximate interval where the zeros of the function $f\\left(x\\right)=\\ln x-\\frac{2}{x}$ lie.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (2,3) | MATH |
[
{
"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 $C_{23}^{3n+1} = C_{23}^{n+6}$ ($n \\in \\mathbb{N}^*$) and $(3-x)^n = a_0 + a_1x + a_2x^2 + \\ldots + a_nx^n$, find the value of $a_0 - a_1 + a_2 - \\ldots + (-1)^n a_n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 256 | MATH |
[
{
"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 $6\\,41G\\,507\\,3H6$ must be divisible by $72$. If $G$ and $H$ each represent a single digit, find the sum of all distinct possible values of the product $GH$ (count each possible value of $GH$ only once, even if it results from multiple $G,$ $H$ pairs).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 42 | MATH |
[
{
"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 $i$ is the imaginary unit, calculate the value of the complex number $\\frac {3+i}{1-i}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1+2i | MATH |
[
{
"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": "Expand and simplify the expression $2(c-2)(c^2 + c(4 - c))$. What is the sum of the coefficients of the expanded form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -8 | MATH |
[
{
"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 all pairs $(x, y)$ of real numbers satisfying the system : $\\begin{cases} x + y = 3 \nx^4 - y^4 = 8x - y \\end{cases}$ \n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (2, 1) | MATH |
[
{
"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 plane $(xOy)$, the parametric equations of line $(l)$ are given by $\\begin{cases} x= \\frac {2 \\sqrt {5}}{5}t \\\\ y=1+ \\frac { \\sqrt {5}}{5}t\\end{cases}$ (where $t$ is the parameter). Line $(l)$ intersects the parabola $y^{2}=4x$ at points $A$ and $B$. The length of the line segment $AB$ is _____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 4 \sqrt {10} | MATH |
[
{
"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 $g(x)=\\frac{x-3}{x^2+cx+d}$, and $g(x)$ has vertical asymptotes at $x=2$ and $x=-1$, find the sum of $c$ and $d$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -3 | MATH |
[
{
"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 $\\{a_n\\}$ be an arithmetic sequence, and $\\{b_n\\}$ be a geometric sequence, with $b_1=a_1^2$, $b_2=a_2^2$, $b_3=a_3^2$ ($a_1<a_2$), and $$\\lim_{n\\rightarrow +\\infty }(b_{1}+b_{2}+\\cdots +b_{n})= \\sqrt {2}+1.$$ Find the first term and the common difference of $\\{a_n\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 \sqrt {2}-2 | MATH |
[
{
"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 random walk of a point starts from the origin on a line and makes \\(a\\) steps to the right, \\(b\\) steps to the left in some order, with \\(a > b\\). The range of the walk is defined as the difference between the highest and lowest coordinates of the point during the walk.\n\na) Find the maximum possible range of the walk.\n\nb) Find the minimum possible range of the walk.\n\nc) How many different sequences of movements are there in which the range of the walk is the maximum possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | b+1 | MATH |
[
{
"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 triangle $\\triangle ABC$, it is known that $\\angle B=60^{\\circ}$ and $b=\\sqrt{3}$. If there is only one triangle that satisfies the conditions, determine the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 0 < a ≤\sqrt{3} \text{ or } a=2 | MATH |
[
{
"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": "Solve for $x$: $$\\sqrt[3]{5x - \\frac{2}{x}} = 3$$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | x = \frac{27 + \sqrt{769}}{10} \text{ or } x = \frac{27 - \sqrt{769}}{10} | MATH |
[
{
"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": "1. Given $\\sin\\alpha + \\cos\\alpha = \\frac{7}{13}$, with $\\alpha \\in (0, \\pi)$, find the value of $\\tan\\alpha$.\n2. Find the minimum value for $y=\\sin 2x + 2\\sqrt{2}\\cos\\left(\\frac{\\pi}{4}+x\\right)+3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2 - 2\sqrt{2} | MATH |