messages
listlengths 3
3
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stringlengths 1
2.25k
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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": "Let \\[z=\\frac{1+i}{\\sqrt{2}}.\\] Calculate the expression \\[\\left(z^{1^3}+z^{2^3}+z^{3^3}+\\dots+z^{{8}^3}\\right) \\cdot \\left(\\frac{1}{z^{1^3}}+\\frac{1}{z^{2^3}}+\\frac{1}{z^{3^3}}+\\dots+\\frac{1}{z^{{8}^3}}\\right).\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 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": "In $\\triangle ABC$, the sides opposite to angles A, B, C are $a$, $b$, $c$ respectively. Given that $B=60^\\circ$, $c=4$.\n(1) If point $M$ is the midpoint of segment $BC$, and $\\frac{AM}{BM} = \\sqrt{3}$, find the value of $a$;\n(2) If $b=6$, find the area of $\\triangle ABC$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2\sqrt{3} + 6\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": "Given $2^{x}-2^{y} \\lt 3^{-x}-3^{-y}$, solve for $\\ln \\left(y-x+1\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \ln(y-x+1) > 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": "As is well known, balance scales reach equilibrium when both pans have the same weight. On one pan of the scales lie 9 identical diamonds, and on the other - 4 identical emeralds. If one more of the same emerald is added to the side with the diamonds, the scales will balance. How many diamonds will balance one emerald? Justify your answer.\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 $x, y>0, \\log_y(x) + \\log_x(y) = \\frac{11}{3}$ and $xy = 128$, compute $\\frac{x+y}{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \sqrt[5]{4} + 8\sqrt[5]{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": "Find the smallest natural number that can be expressed as the sum of 2002 natural addends with the same sum of digits and as the sum of 2003 natural addends with the same sum of digits.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 10010 | 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 60 cards are dealt to 9 people as evenly as possible, how many people will end up with fewer than 7 cards?\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 the line $l$: $mx - m^2y - 1 = 0$, find the equation of the line perpendicular to $l$ with the foot of the perpendicular being point $P(2, 1)$.\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": "a. Find all integer values of \\(a\\) such that equation \\(x^2 + ax + 1 = 0\\) does not have real solutions in \\(x\\).\n\nb. Find all pairs of integers \\((a, b)\\) such that both equations\n\\[ x^2 + ax + b = 0 \\quad \\text{and} \\quad x^2 + bx + a = 0 \\]\nhave no real solutions in \\(x\\).\n\nc. How many ordered pairs \\((a, b)\\) of positive integers satisfying \\(a \\leq 8\\) and \\(b \\leq 8\\) are there, such that each of the equations\n\\[ x^2 + ax + b = 0 \\quad \\text{and} \\quad x^2 + bx + a = 0 \\]\nhas two unique real solutions in \\(x\\)?\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": "For a nonnegative integer $n$, let $r_7(n)$ represent the remainder when $n$ is divided by $7$. For instance, $r_7(10) = 3$.\n\nWhat is the $15^\\text{th}$ entry in an ordered list of all nonnegative integers $n$ that satisfy $$r_7(3n) \\le 3~?$$ (Note that the first entry in this list is $0$.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 22 | 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 library shelf has three layers. The first layer contains $3$ different math books, the second layer contains $5$ different literature books, and the third layer contains $8$ different English books. Determine the number of different ways to select one book from the shelf.\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": "How many different sequences of 17 coin tosses will contain exactly three HH, two HT, five TH, and six TT subsequences?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2940 | 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 $x^{15} + 1$ is divided by $x + 1$, determine the remainder.\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": "Given the initial revenue of 2.5 million yuan in January, and the planned revenue for the first quarter of 9 million yuan, the monthly average growth rate of the revenue in February and March is denoted by $x$. Determine the correct equation that represents this situation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | D: 250+250(1+x)+250(1+x)^2=900 | 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 an equilateral triangle \\( T \\) of side length 12. Matthew cuts \\( T \\) into \\( N \\) smaller equilateral triangles, each of which has side length 1, 3, or 8. Compute the minimum possible value of \\( N \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | N = 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": "Given the sequence $\\{a_n\\}$, $a_1=3$, and $a_{n+1}-a_n=2$ ($n\\in\\mathbb{N}^*$), calculate the value of $a_{10}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 21 | 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 $\\mathcal{S}$ be the set of all positive integers which are both a multiple of $3$ and have at least one digit that is a $1$ . For example, $123$ is in $\\mathcal{S}$ and $450$ is not. The probability that a randomly chosen $3$ -digit positive integer is in $\\mathcal{S}$ can be written as $\\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .\n\n*Proposed by GammaZero*\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 491 | 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 7th term of an arithmetic sequence of 15 terms where the first term is 3 and the last term is 72?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 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": "The residents of Madbury decided to surround the monument adorning their town with elegant columns. It turned out that if the columns are placed 10 cm apart, 150 columns are not enough, but if they are placed 30 cm apart, 70 columns remain. How many columns were there?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 180 | 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 an odd function with a period of 4, and $f(x) = 2x(1-x)$ when $0 \\leq x \\leq 1$, then $f(2015.5) = \\_\\_\\_\\_\\_\\_$.\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": "Given \\( x \\in \\left[-\\frac{\\pi}{12}, -\\frac{\\pi}{3} \\right] \\), find the maximum value of \\( y = -\\tan \\left(x + \\frac{2\\pi}{3}\\right) - \\tan \\left(x + \\frac{\\pi}{6}\\right) + \\cos \\left(x + \\frac{\\pi}{6}\\right) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{11}{6} \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": "Given that $x_{1}$ and $x_{2}$ are the two roots of the quadratic equation $-2x^{2}+x+5=0$, find the value of the algebraic expression $x_{1}^{2}x_{2}+x_{1}x_{2}^{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -\frac{5}{4} | 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 a geometric sequence composed of positive numbers, and $a_3 \\cdot a_7 = 64$. Calculate the value of $\\log_{2}a_1 + \\log_{2}a_2 + \\ldots + \\log_{2}a_9$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 27 | 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 equations:<br/>$(1)x^{2}-4x-1=0$;<br/>$(2)\\left(x+3\\right)^{2}=x+3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | x_{1}=-3, \quad x_{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": "A circle has a radius of 6 inches. The distance from the center of the circle to chord $PQ$ is 5 inches. How many inches long is chord $PQ$? 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"
}
] | 2\sqrt{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": "A right triangle has legs measuring 24 inches and 32 inches. What is the length of the hypotenuse, in inches?\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": "In $\\triangle ABC$, if the three sides $a$, $b$, $c$ and the area $S$ satisfy $S=a^{2}-(b-c)^{2}$, then $\\sin A=$ \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \sin A = \frac{8}{17} | 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 universal set $I=\\mathbb{R}$, set $A=\\{x\\in\\mathbb{R}|\\frac{x+1}{x+3}\\leqslant\\frac{1}{2}\\}$, and set $B$ is the solution set of the inequality $2^{|x+1|}<4$, find $A\\cap(C_{I}B)$.\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": "Given that $\\sqrt{2+\\frac{2}{3}}=2\\sqrt{\\frac{2}{3}}$, $\\sqrt{3+\\frac{3}{8}}=3\\sqrt{\\frac{3}{8}}$, $\\sqrt{4+\\frac{4}{15}}=4\\sqrt{\\frac{4}{15}},\\cdots ,\\sqrt{8+\\frac{a}{t}}=8\\sqrt{\\frac{a}{t}},a,t\\in \\mathbb{R}_{+}$, calculate $a+t$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 71 | 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 $g(x)=(-x^{2}+5x-3)e^{x}$ ($e$ is the base of the natural logarithm), find the equation of the tangent line to the function $y=g(x)$ at $x=1$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 4ex-y-3e=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": "1. Given $x > 0$, $y > 0$, and $x+2y=8$, find the maximum value of $xy$.\n2. Given $x > -1$, find the minimum value of the function $y=x+ \\frac {4}{x+1}+6$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | y_{\text{min}} = 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": "Given the function $f(x)= \\sqrt {3}\\sin ^{2}ωx+\\sin ωx\\cos ωx- \\frac { \\sqrt {3}}{2} (ω > 0)$, and the distance from one symmetry center of the graph of $y=f(x)$ to the nearest symmetry axis is $\\frac {π}{4}$.\n(1) Find the value of $ω$;\n(2) Find the value of $x$ when $f(x)$ takes the minimum value in the interval $[0, \\frac {π}{2}]$.\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": "Given that $i$ is the imaginary unit, if $|a-2+\\frac{4+3i}{1+2i}| = \\sqrt{3}a$, then the real number $a$ equals ______.\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": "Given $\\sin(\\alpha-\\beta) = \\frac{3}{5}$, $\\sin(\\alpha+\\beta) = -\\frac{3}{5}$, and $\\alpha-\\beta \\in \\left(\\frac{\\pi}{2}, \\pi\\right)$, $\\alpha+\\beta \\in \\left(\\frac{3\\pi}{2}, 2\\pi\\right)$, find the value of $\\cos 2\\beta$.\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": "Given that a car brand's 4S store is selling 5 types of cars through live streaming, each type for one day a week, calculate the probability that the live streaming promotions for types A and B are not consecutive.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \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": "Given in $\\triangle ABC$, $\\sin A= \\frac {3}{5}$, $\\cos B=- \\frac {5}{13}$. \n$(1)$ Find the value of $\\sin 2A$; \n$(2)$ Find the value of $\\cos C$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac {56}{65} | 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 given plane, points $A$ and $B$ are $12$ units apart. Calculate the number of points $C$ such that the perimeter of $\\triangle ABC$ is $60$ units and the area of $\\triangle ABC$ is $120$ square units.\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 prime number \\( p \\) is such that the number \\( p + 25 \\) is the seventh power of a prime number. What can \\( p \\) be? List all possible options.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 103 | 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": "Evaluate the expression $\\sqrt{80} - 3\\sqrt{20} + \\frac{\\sqrt{500}}{\\sqrt{5}} + 2\\sqrt{45}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 4\sqrt{5} + 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": "Find all solutions to the inequality \\[\\frac{(3x-5)(x-2)(x+1)}{2x} \\ge 0.\\] (Give your answer in interval notation.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | (-1, 0) \cup (0, 2] \cup \left(\frac{5}{3}, \infty\right) | 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 terminal side of angle $\\alpha$ is in the fourth quadrant, and $2\\sin 2\\alpha + 1 = \\cos 2\\alpha$, calculate $\\tan({\\alpha-\\frac{\\pi}{4}})$.\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": "Evaluate $\\lfloor e^2 \\rfloor$, where $e$ is Euler's number.\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 a rectangle's diagonal measures d. If the length of the rectangle is three times its width, calculate the area of the rectangle.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{3d^2}{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": "Find the number of ordered pairs of positive integers $(x, y)$ that satisfy the equation\n$$\nx \\sqrt{y} + y \\sqrt{x} + \\sqrt{2009 x y} - \\sqrt{2009 x} - \\sqrt{2009 y} - 2009 = 0.\n$$\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": "In a right triangle with base \\(b\\), height \\(h\\), hypotenuse \\(c\\), and the radius of the inscribed circle \\(r\\), find the ratio of the area of the circle to the area of the triangle.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{2\pi \frac{b^2h^2}{(b+h+\sqrt{b^2+h^2})^2}}{b+h+\sqrt{b^2+h^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 $F_1$ and $F_2$ are the left and right foci of the ellipse $C$: $\\frac{x^2}{4} + y^2 = 1$, and point $P$ is on $C$ with $|PF_1| = 3|PF_2|$, find the value of $\\cos \\angle F_1PF_2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -\frac{1}{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": "There are 5 people each holding 5 different jobs. Now, we need to make adjustments, and after the adjustment, at least 2 people must be doing different jobs from before. How many different adjustment methods are there?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 119 | 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": "Mario has a deck of seven pairs of matching number cards and two pairs of matching Jokers, for a total of 18 cards. He shuffles the deck, then draws the cards from the top one by one until he holds a pair of matching Jokers. The expected number of complete pairs that Mario holds at the end (including the Jokers) is \\(\\frac{m}{n}\\), where \\(m, n\\) are positive integers and \\(\\operatorname{gcd}(m, n) = 1\\). Find \\(100m + n\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 1003 | 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 heights of all the players in a team are as follows (in cm): \n178, 179, 181, 182, 176, 183, 180, 183, 175, 181, 185, 180, 184. \nWhat is the average height of the players in this team (rounded to the nearest cm)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 180 \text{ cm} | 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": "Chinese outstanding traditional culture is the \"root\" and \"soul\" of the Chinese nation, which is the cultural root and gene that we must inherit from generation to generation. In order to inherit the outstanding traditional culture, a certain school purchased several sets of \"Romance of the Three Kingdoms\" and \"Water Margin\" comic books for each class. The price of each set of \"Romance of the Three Kingdoms\" comic books is $60 more expensive than the price of each set of \"Water Margin\" comic books. It is known that the school spent $3600 on \"Romance of the Three Kingdoms\" comic books and $4800 on \"Water Margin\" comic books. The number of sets of \"Romance of the Three Kingdoms\" comic books purchased is half the number of sets of \"Water Margin\" comic books purchased. Find the price of each set of \"Water Margin\" comic books.\n- $(1)$ Let the price of each set of \"Water Margin\" comic books be $x$ dollars. Express the price of each set of \"Romance of the Three Kingdoms\" comic books in terms of $x$: The price of each set of \"Romance of the Three Kingdoms\" comic books is ______ dollars.\n- $(2)$ Write down the equation and complete the solution to this problem.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 120 \text{ dollars} | 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 space rectangular coordinate system, $A(1,1,1)$, $B(2,3,4)$, and a normal vector of plane $BCD$ is $(-1,2,1)$. The distance from point $A$ to plane $BCD$ is ____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \sqrt{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": "(10 points) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 459 and 357, and verify it using the method of successive subtraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 51 | 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 number of integers that we can choose from the set $\\{1, 2, 3, \\ldots, 2017\\}$ such that the difference between any two of them is not a prime number?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 505 | 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": "Points $A=(4,15)$ and $B=(14,9)$ lie on circle $\\omega$ in the plane. Suppose that the tangent lines to $\\omega$ at $A$ and $B$ intersect at a point on the $x$-axis. What is the area of $\\omega$?\nA) $40\\pi$\nB) $39\\pi$\nC) $41\\pi$\nD) $42\\pi$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 40\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": "A spinner with seven equal sectors labeled from 1 to 7 is used in a game between two players, Alice and Bob. They each spin the spinner once. Alice wins if the absolute difference between their numbers is less than 4. Otherwise, Bob wins. Determine the probability that Alice wins.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | \frac{37}{49} | 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 the set $A=\\{x\\ |\\ -1 \\leq x \\leq 6\\}$ and $B=\\{x\\ |\\ m-1 \\leq x \\leq 2m+1\\}$. Given that $B \\subseteq A$,\n\n(1) Find the range of real numbers $m$.\n(2) When $x \\in \\mathbb{N}$ (natural numbers), find the number of subsets of the set $A$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 2^7 = 128 | 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": "Subtract the sum of the first 180 positive odd numbers from the sum of the first 180 positive even numbers.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 180 | 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 initial pile of 18 stones is shared between two players, with each player taking a number of stones between 1 and 4 at a time. Determine the minimum number of stones the first player must pick to guarantee a win.\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": "An ancient human tribe had a hierarchy with one king, 2 knights (knight A and knight B), each knight having 3 squires. If the tribe at one point had 15 members, what is the number of different ways to choose this leadership structure? That is, in how many ways can we choose a king, 2 knights, and three squires for each knight?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 27392400 | 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 necklace consists of 50 blue beads and some quantity of red beads. It is known that on any segment of the necklace containing 8 blue beads, there are at least 4 red beads. What is the minimum number of red beads that can be in this necklace? (The beads in the necklace are arranged cyclically, meaning the last bead is adjacent to the first one.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | 29 | 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 series \\(-\\frac{3}{1!} + \\frac{7}{2!} - \\frac{13}{3!} + \\frac{21}{4!} - \\frac{31}{5!} + \\dots + \\frac{1994^2 + 1994 + 1}{1994!}\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
},
{
"content": "I am a dummy message",
"role": "user"
}
] | -1 + \frac{1995}{1994!} | MATH |