Search is not available for this dataset
data_source stringclasses 10 values | prompt listlengths 2 2 | ability stringclasses 2 values | reward_model dict | extra_info dict | ground_truth stringlengths 1 79.2M | messages listlengths 1 1 | dataset stringclasses 1 value |
|---|---|---|---|---|---|---|---|
numina_synthetic_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]... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 91 | [
{
"content": "Compute\n\\[\\cos^2 0^\\circ + \\cos^2 2^\\circ + \\cos^2 4^\\circ + \\dots + \\cos^2 180^\\circ.\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{4}{3} | [
{
"content": "Compute: $(\\pi-3.14)^{0}+3^{-1}=\\_\\_\\_\\_\\_\\_.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2px^2 - \\beta xy + \\alpha y^2 - 2p \\alpha x = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2px^2 - \beta xy + \alpha y^2 - 2p \alpha x = 0 | [
{
"content": "Given the parabola \\( y^{2} = 2px \\) and a point \\( A \\) in its plane. From the vertex \\( O \\) of the parabola we draw an arbitrary chord \\( OB \\); let \\( C \\) be the projection of the point \\( B \\) on the tangent at the vertex. What is the locus of the intersection point \\( M \\) of ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 | [
{
"content": "The remainder of \\\\(2^{30}+3\\\\) divided by \\\\(7\\\\) is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{4} | [
{
"content": "A person rolls two dice simultaneously and gets the scores $a$ and $b$. The eccentricity $e$ of the ellipse $\\frac{y^2}{a^2} + \\frac{x^2}{b^2} = 1$ satisfies $e \\geq \\frac{\\sqrt{3}}{2}$. Calculate the probability that this event occurs.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "88\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 88\pi | [
{
"content": "In a plane, four circles with radii $2, 4, 6,$ and $8$ are tangent to line $\\ell$ at the same point $A$. These circles may be placed on either side of $\\ell$. Region $T$ consists of all points that lie inside exactly one of these circles. Find the maximum possible area of region $T$.\n\nPresent ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "2\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2\pi | [
{
"content": "Three of the four vertices of a rectangle are $(5, 11)$, $(16, 11)$, and $(16, -2)$. What is the area of the intersection of this rectangular region and the region inside the graph of the equation $\\frac{(x - 5)^2}{16} + \\frac{(y + 2)^2}{4} = 1$? Express your answer in terms of $\\pi$.\n\nPresen... | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "n \\le 10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | n \le 10 | [
{
"content": "Find all positive integer $n(\\ge 2)$ and rational $\\beta \\in (0,1)$ satisfying the following:\nThere exist positive integers $a_1,a_2,...,a_n$ , such that for any set $I \\subseteq \\{1,2,...,n\\}$ which contains at least two elements, $$ S(\\sum_{i\\in I}a_i)=\\beta \\sum_{i\\in I}S(a... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{16}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{16}{3} | [
{
"content": "Define the solid \\( T \\) consisting of all points \\((x, y, z)\\) such that \\( |x| + |y| \\leq 2 \\), \\( |x| + |z| \\leq 2 \\), and \\( |y| + |z| \\leq 2 \\). Calculate the volume of \\( T \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "9604",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 9604 | [
{
"content": "Evaluate \\(98 \\times 98\\) in your head.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{4} | [
{
"content": "What is the probability that a positive integer less than or equal to 36 is a factor of 36? Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "103,680",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 103,680 | [
{
"content": "How many four-character license plates can be made if each license plate consists of a consonant, followed by a vowel (which may repeat), followed by another vowel, and ending with a character which can be a digit or one of the two special symbols '@' and '#'? (Consider only A, E, I, O, U, and Y a... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{127}{24}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{127}{24} | [
{
"content": "Given the function $g(x) = \\frac{6x^2 + 11x + 17}{7(2 + x)}$, find the minimum value of $g(x)$ for $x \\ge 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Given the sequence $\\{a_n\\}$ with the general term formula $a_n = 5(\\frac{2}{5})^{2n-2} - 4(\\frac{2}{5})^{n-1} (n \\in \\mathbb{N}^*)$, where the maximum term is the $p$-th term and the minimum term is the $q$-th term, calculate the value of $q - p$.\n\nPresent the answer in LaTex format: \\bo... | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "n = 3, 5, 17, 257, 65537",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | n = 3, 5, 17, 257, 65537 | [
{
"content": "Determine all integers $n \\ge 3$ whose decimal expansion has less than $20$ digits, such that every quadratic non-residue modulo $n$ is a primitive root modulo $n$ .\n\n*An integer $a$ is a quadratic non-residue modulo $n$ , if there is no integer $b$ such that $a - b^2$ is divisibl... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x-y+2=0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x-y+2=0 | [
{
"content": "Find the equation of the tangent line to the curve $y=x^{3}-2x+4$ at the point $(1,3)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-a > a^{2} > -a^{2} > a",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -a > a^{2} > -a^{2} > a | [
{
"content": "If $a \\in \\mathbb{R}$ and $a^{2}+a < 0$, then the order of $a$, $a^{2}$, $-a$, $-a^{2}$ is __________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "92 \\text{ moves}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 92 \text{ moves} | [
{
"content": "a) On each of the squares in the top and bottom rows of an $8 \\times 8$ chessboard, there is a piece: white pieces on the bottom, black pieces on the top. In one move, it is allowed to move any piece to an adjacent free square either vertically or horizontally. What is the minimum number of moves... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -4 | [
{
"content": "Given the sequence $a_{1}=1,a_{2}=5,a_{n+2}=a_{n+1}-a_{n}(n∈N^{∗})$, calculate the value of $a_{2016}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{21}{32}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{21}{32} | [
{
"content": "John has six children. What is the probability that at least half of them are girls? (Assume the probability of having a boy or a girl is equal.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "1.3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1.3 | [
{
"content": "Consider another cubic equation $20x^3 - 34x^2 + 15x - 1 = 0$. Assume its roots, $a, b,$ and $c$, are distinct and lie strictly between $0$ and $1$. Compute the sum:\n\\[ \\frac{1}{1-a} + \\frac{1}{1-b} + \\frac{1}{1-c} \\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 | [
{
"content": "Given that real numbers $x_{1}$ and $x_{2}$ are the two roots of the equation $-x^{2}+3x=0$, find $x_{1}x_{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x-y-1=0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x-y-1=0 | [
{
"content": "Given a parabola with its vertex at the origin and focus on the y-axis, which passes through point P(2,1).\n\n1. Find the standard equation of the parabola.\n2. Determine the equation of the line l through point P that intersects the parabola at only one point.\n\nPresent the answer in LaTex forma... | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{L}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{L}{2} | [
{
"content": "Let $L$ be a positive constant. For a point $P(t,\\ 0)$ on the positive part of the $x$ axis on the coordinate plane, denote $Q(u(t),\\ v(t))$ the point at which the point reach starting from $P$ proceeds by distance $L$ in counter-clockwise on the perimeter of a circle passing the poi... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{\\sqrt{30}}{100}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\sqrt{30}}{100} | [
{
"content": "When the decimal point of a certain positive decimal number is moved three places to the right, the new number is three times the reciprocal of the original number. What is the original number?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "8 \\sqrt{2} \\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 \sqrt{2} \pi | [
{
"content": "Find the smallest positive period of the function \\( f(x) = \\cos(\\sqrt{2} x) + \\sin\\left(\\frac{3}{8} \\sqrt{2} x\\right) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 50 | [
{
"content": "In a frequency distribution histogram of a sample with a capacity of $300$, there are a total of $9$ small rectangles. If the area of the middle rectangle is equal to $\\dfrac{1}{5}$ of the sum of the areas of the other $8$ rectangles, then the frequency of the middle group is ______.\n\nPresent t... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{39}{210}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{39}{210} | [
{
"content": "An element is randomly chosen from among the first $20$ rows of Pascal's Triangle. What is the probability that the value of the element chosen is $1$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 | [
{
"content": "For how many values of the digit $A$ is it true that $75$ is divisible by $A$ and $536{,}1A4$ is divisible by $4$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "m = 33, n = 61",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | m = 33, n = 61 | [
{
"content": "Find two natural numbers \\( m \\) and \\( n \\), given that \\( m < n < 2m \\) and \\( mn = 2013 \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "34.15\\ \\text{USD}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 34.15\ \text{USD} | [
{
"content": "Alice is visiting the UK and decides to buy a book priced at £25 and a sandwich for £3. If one U.S. dollar is worth £0.82, how much money, in USD, does Alice have to spend for both items combined?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{31}{32}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{31}{32} | [
{
"content": "In the positive-term geometric sequence $\\{a\\_n\\}$, the sum of the first $n$ terms is $S\\_n$. Given that $a\\_5 = \\frac{1}{2}$ and $a\\_6 + a\\_7 = 3$, find $S\\_5$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "81y^{16}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 81y^{16} | [
{
"content": "Simplify \\((3y^4)^4\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{2} | [
{
"content": "A sphere-shaped balloon with a radius of 2 feet is filled with helium. This helium is then evenly transferred into 64 smaller sphere-shaped balloons. What is the radius of each of the smaller balloons, in feet?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{7}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \sqrt{7} | [
{
"content": "Given vectors $\\overrightarrow{a}=(\\sqrt{3},k)$, $\\overrightarrow{b}=(0,-1)$, $\\overrightarrow{c}=(1,\\sqrt{3})$. \n$(Ⅰ)$ If $\\overrightarrow{a}\\perp \\overrightarrow{c}$, find the value of $k$. \n$(Ⅱ)$ When $k=1$, and $\\overrightarrow{a}-\\lambda \\overrightarrow{b}$ is collinear with $\... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "Given the function $f(x)=\\frac{1}{2}\\cos (\\omega x+ \\phi )+1(\\omega > 0)$, determine the minimum value of $\\omega$ such that its graph has a symmetry axis along the line $x=\\frac{\\pi }{3}$ and $f(\\frac{\\pi }{12})=1$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{n}{2(n+2)}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{n}{2(n+2)} | [
{
"content": "Given an arithmetic sequence $\\{a\\_n\\}$ with a non-zero common difference, let $S\\_n$ represent the sum of its first $n$ terms. The first term $a\\_1$ is 2, and $a\\_1$, $a\\_2$, $a\\_4$ form a geometric sequence.\n\n(1) Find the general term formula for the sequence $\\{a\\_n\\}$.\n\n(2) If $... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "P(B) = 0.9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | P(B) = 0.9 | [
{
"content": "In an opaque box, there are three white balls and two black balls with distinct identifiers. The white balls are labeled $a_1$, $a_2$, $a_3$, and the black balls are labeled $b_1$, $b_2$. Two balls are drawn at random from the box.\n(1) List all the possible different outcomes;\n(2) Calculate the ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "374",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 374 | [
{
"content": "Liam has more than $\\$6$ but less than $\\$20$ worth of nickels. When he puts his nickels in stacks of 4, he has 2 left over. When he puts them in stacks of 5, he has 3 left over. When he puts them in stacks of 6, he also has 4 left over. How many nickels does Liam have?\n\nPresent the answer in ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -2 | [
{
"content": "The imaginary part of the complex number $z=\\frac{2+i}{i}$ (where $i$ is the imaginary unit) is what value?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{71}{90}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{71}{90} | [
{
"content": "What is the probability that the square root of a randomly selected two-digit whole number is less than nine? Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Determine how many integer values of $n$ satisfy the inequality $(n-2)(n+4)(n-3) < 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "2 \\sin 5x \\cos 2x",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 \sin 5x \cos 2x | [
{
"content": "Express \\(\\sin 3x + \\sin 7x\\) as a product of trigonometric functions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 49 | [
{
"content": "Odell and Kershaw run for $45$ minutes on a circular track, with Odell running clockwise at $260 m/min$ on the inner lane with a radius of $70$ meters, and Kershaw running counterclockwise at $320 m/min$ on the outer lane with a radius of $80$ meters. Determine the number of times after the start ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "The correct answer is **B) 10**.",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The correct answer is **B) 10**. | [
{
"content": "In a survey of a classroom, students were asked about their favorite type of snack. The results are shown in the table below, but the total number of students, $N$, is not indicated. Determine the smallest possible value of $N$ that allows all the percentages to serve as representations of the who... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "19.5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 19.5 | [
{
"content": "After replacing both the numerator and the denominator of a fraction with new numbers, a student incremented each by 8, resulting in a fraction value of $\\frac{2}{5}$. If the original numerator was 3, what was the original denominator?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 240 | [
{
"content": "Points $A$, $B$, $C$, and $T$ are in space such that each of $\\overline{TA}$, $\\overline{TB}$, and $\\overline{TC}$ is perpendicular to the other two. If $TA = 8$, $TB = 15$, and $TC = 12$, what is the volume of pyramid $TABC$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{5}{26}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{5}{26} | [
{
"content": "If $\\sin x = 5 \\cos x,$ then what is the value of $\\sin x \\cos x$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{197}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{197}{2} | [
{
"content": "Given $f(x)=4x^{5}+3x^{4}+2x^{3}-x^{2}-x-\\frac{1}{2}$, use Horner's method to find $f(-2)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\exists x_{0} \\in \\mathbb{R}, \\sin x_{0} < -1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \exists x_{0} \in \mathbb{R}, \sin x_{0} < -1 | [
{
"content": "Given proposition $p$: $\\forall x \\in \\mathbb{R}$, $\\sin x \\geqslant -1$, determine $\\neg p$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -12 | [
{
"content": "Given $2x-3y+6=0$, then $6x-9y+6=\\_\\_\\_\\_\\_\\_$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "8.5 + \\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8.5 + \frac{\sqrt{2}}{2} | [
{
"content": "Point $P$ lies on the diagonal $AC$ of rectangle $ABCD$ with $AB = 15$ and $BC = 8$, with $AP > CP$. Let $O_{1}$ and $O_{2}$ be the circumcenters of triangles $ABP$ and $CDP$ respectively. Given that $\\angle O_{1}PO_{2} = 90^{\\circ}$, find the exact length of $AP$.\n\nPresent the answer in LaTex... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{100}{9}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{100}{9} | [
{
"content": "The function $g(x)$ satisfies\n\\[g(xy) = \\frac{g(x)}{y^2}\\] for all positive real numbers $x$ and $y.$ If $g(50) = 25,$ find $g(75).$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "B) -78",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | B) -78 | [
{
"content": "Evaluate the expression \\(3 - (-3)^{3 - (-1)}\\).\nA) -81\nB) -78\nC) 82\nD) 84\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{3ab}{\\sqrt{a^4 + 7a^2b^2 + b^4}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{3ab}{\sqrt{a^4 + 7a^2b^2 + b^4}} | [
{
"content": "If\n\\[\\tan x = \\frac{3ab}{a^2 - b^2},\\]where $a > b > 0$ and $0^\\circ < x < 90^\\circ,$ then find $\\sin x$ in terms of $a$ and $b.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 29 | [
{
"content": "In my drawer, I have 13 distinguishable socks: 5 white, 5 brown, and 3 blue. In how many ways can I select a pair of socks such that the socks are of different colors and both socks come from either odd or even-numbered positions within their color set?\n\nPresent the answer in LaTex format: \\box... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "B) 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | B) 1 | [
{
"content": "Simplify the expression: \\(1 - \\frac{1}{2 + \\sqrt{5}} + \\frac{1}{2 - \\sqrt{5}}\\).\nA) 0\nB) 1\nC) 2\nD) 3\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{4465}{144}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{4465}{144} | [
{
"content": "Find the real root of the equation \\[\\sqrt{x+4} + \\sqrt{x+6} = 12.\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3^{120}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3^{120} | [
{
"content": "The sequence $\\{a_n\\}$ is a geometric progression with a common ratio of 3, and the product of its terms $a_1a_4a_7…a_{28} = 3^{100}$. Find the product $a_3a_6a_9…a_{30}$.\n\nA) $3^{100}$\nB) $3^{110}$\nC) $3^{120}$\nD) $3^{130}$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -15 | [
{
"content": "Given $f(x)=(1+x)^6(1-x)^5$, find the coefficient of $x^2$ in the derivative $f'(x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "123",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 123 | [
{
"content": "In city $\\mathrm{N}$, there are exactly three monuments. One day, a group of 42 tourists arrived in this city. Each tourist took no more than one photograph of each of the three monuments. It turned out that any two tourists together had photographs of all three monuments. What is the minimum num... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\pi}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\pi}{4} | [
{
"content": "Simplify the expression $\\dfrac{2\\cos^2\\alpha - 1}{2\\tan(\\frac{\\pi}{4}-\\alpha)\\sin^2(\\frac{\\pi}{4}+\\alpha)}$.\nAlso, given that both $\\alpha$ and $\\beta$ are acute angles, and $\\sin\\alpha = \\frac{2\\sqrt{5}}{5}, \\sin\\beta = \\frac{\\sqrt{10}}{10}$, find the value of $\\alpha - \\... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 10 | [
{
"content": "What is the minimum value of the expression $2x^2 + 3y^2 - 8x + 6y + 25$ for real $x$ and $y$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "A \\geq 0, B \\geq 0, C \\geq 0, A^2 + B^2 + C^2 \\leq 2(AB + AC + BC)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A \geq 0, B \geq 0, C \geq 0, A^2 + B^2 + C^2 \leq 2(AB + AC + BC) | [
{
"content": "Find real numbers $A, B, C$ such that for any real numbers $x, y, z$, the following inequality holds:\n$$\nA(x-y)(x-z)+B(y-z)(y-x)+C(z-x)(z-y) \\geq 0\n$$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{96}{100} = \\frac{24}{25}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{96}{100} = \frac{24}{25} | [
{
"content": "The length of the longer side of rectangle \\( R \\) is \\( 20\\% \\) more than the length of a side of square \\( S \\). The length of the shorter side of rectangle \\( R \\) is \\( 20\\% \\) less than the length of a side of square \\( S \\). What is the ratio of the area of rectangle \\( R \\) ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "45^{\\circ}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 45^{\circ} | [
{
"content": "Given non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $\\overrightarrow{b}= \\sqrt{2}$, and $(\\overrightarrow{a}- \\overrightarrow{b})\\cdot(\\overrightarrow{a}+ \\overrightarrow{b})= \\frac{1}{4}$.\n\n(I) Find $|\\overrightarrow{a}|$;\n\n(II) When $\\overrightarrow{a}... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 9 | [
{
"content": "Determine for which positive integer $n$ the value of the expression \n\\[\\frac{n}{3} + \\frac{27}{n}\\]\nis minimized.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{-1032192}{1874161}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{-1032192}{1874161} | [
{
"content": "\\[\n\\begin{align*}\n3a + 4b + 6c + 8d &= 48 \\\\\n4(d+c) &= b \\\\\n4b + 2c &= a \\\\\nc - 2 &= d \\\\\n\\end{align*}\n\\] \nGiven the above system of equations, find \\( a \\cdot b \\cdot c \\cdot d \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\dfrac{5x^2}{1}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \dfrac{5x^2}{1} | [
{
"content": "A trapezoid has one base equal to four times its height, $x$, and the other base is six times as long as the height. Write the expression for the area of the trapezoid as a common fraction in terms of the height $x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(2, 3)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (2, 3) | [
{
"content": "Find the interval of increase for the function $y=\\log_{\\frac{1}{3}}(-3+4x-x^2)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "If $x - y = 10$ and $x + y = 14$, what is the value of $y$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{9}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{9}{2} | [
{
"content": "Given vectors $\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}=\\overrightarrow{0}$, $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=|\\overrightarrow{c}|=2$, then $\\overrightarrow{a}\\cdot \\overrightarrow{b}+\\overrightarrow{b}\\cdot \\overrightarrow{c}+\\overrightarrow{c}\\cdot \... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{3 \\sqrt{10}}{10}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{3 \sqrt{10}}{10} | [
{
"content": "Given $ \\alpha \\in \\left(0, \\frac{\\pi}{2}\\right) $ and $ \\tan \\alpha = 2 $, find $ \\cos\\left(\\alpha - \\frac{\\pi}{4}\\right) = $ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "A) \\( c = -a^2 + 2b - 2 \\)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A) \( c = -a^2 + 2b - 2 \) | [
{
"content": "Consider the quadratic equations $x^2 + ax + b = 0$ and $x^2 + cx + d = 0$ where the roots of the first equation $\\alpha$ and $\\beta$ are transformed into the roots $\\alpha^2 + 1$ and $\\beta^2 + 1$ of the second equation. Determine the relation between $c$ and $a, b$.\nA) \\( c = -a^2 + 2b - 2... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "4200",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4200 | [
{
"content": "In a shooting competition, ten clay targets are arranged in three hanging columns with four targets in the first column, three in the second column, and three in the third column. A shooter must follow these rules:\n1) The shooter selects one column from which a target will be broken.\n2) The shoo... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "37",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 37 | [
{
"content": "Find the sum of the coefficients in the polynomial \\[ -3(x^8 - 2x^5 + 4x^3 - 6) + 5(x^4 + 3x^2) - 2(x^6 - 5) \\].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 6 | [
{
"content": "Given the dataset 5, 9, 9, 3, 4, determine the average value.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[4,+\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [4,+\infty) | [
{
"content": "The monotonic increasing interval of the function $f(x)=\\sqrt{x^{2}-2x-8}$ is $\\boxed{[ ? ]}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "D) \\( \\sqrt{2000} \\)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | D) \( \sqrt{2000} \) | [
{
"content": "Solve the complex equation \\( z(z+i)(z+4i) = 1500i \\). If one of the zeros is of the form \\( a+bi \\) where \\( a \\) and \\( b \\) are positive real numbers, find \\( a \\).\nA) \\( \\sqrt{100} \\)\nB) \\( \\sqrt{500} \\)\nC) \\( \\sqrt{1500} \\)\nD) \\( \\sqrt{2000} \\)\n\nPresent the answer ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "In the polar coordinate system, the intersection points of two curves $C_{1}: \\rho\\sin(\\theta + \\frac{\\pi}{4}) = 1$ and $C_{2}: \\rho = \\sqrt{2}$ are $A$ and $B$. Determine the value of $|AB|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{6}{42}, \\,\\frac{5}{42}, \\,\\frac{4}{42}, \\,\\frac{3}{42}, \\,\\frac{2}{42}, \\,\\frac{1}{42},\\, 0 \\, \\text{liters}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{6}{42}, \,\frac{5}{42}, \,\frac{4}{42}, \,\frac{3}{42}, \,\frac{2}{42}, \,\frac{1}{42},\, 0 \, \text{liters} | [
{
"content": "Seven dwarfs sat at a round table, each with a mug containing a total of half a liter of milk. (Some of the mugs might have been empty.) One of the dwarfs stood up and distributed the milk in his mug equally to the others. Then, the dwarfs to his right took turns doing the same. After the seventh ... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Alice and Bob play a game involving two thousand and eleven \\(2011 \\times 2011\\) grids distributed between them: 1 to Bob and the other 2010 to Alice. Behind closed doors, they fill their grids with the numbers \\(1, 2, \\ldots, 2011^2\\) such that the numbers increase strictly across rows (lef... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -1 | [
{
"content": "Simplify the following expressions:\n(1) $sin \\alpha \\cdot cos \\alpha \\cdot (tan \\alpha + cot \\alpha)$;\n(2) $\\frac{\\sqrt{1 - 2sin\\theta cos\\theta}}{sin\\theta - \\sqrt{1 - sin^2\\theta}}$, where $\\theta \\in (0, \\frac{\\pi}{4})$.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | PRIME-Eurus-2-RL-Data |
numina_amc_aime | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{4}{3} | [
{
"content": "Given the equation $3x^2 - 4x + k = 0$ with real roots. Find the value of $k$ for which the product of the roots of the equation is a maximum.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "200 \\text{ kWh}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 200 \text{ kWh} | [
{
"content": "A partial information of a resident's electricity bill for a certain month is provided as shown in the table below:\n\n| Item | Value |\n|------|-------|\n| Type of Invoice | Residential Electricity Bill |\n| Billing Period | One month |\n| Electricity Usage (kWh) | Price per unit (yuan/kWh) |\n| ... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\begin{cases}\n c_{2n-1} = 9n^2 - 9n + 2, \\\\\n c_{2n} = 9n^2 - 1.\n\\end{cases}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \begin{cases}
c_{2n-1} = 9n^2 - 9n + 2, \\
c_{2n} = 9n^2 - 1.
\end{cases} | [
{
"content": "For the sequence \\( \\{a_{n}\\} \\), the two adjacent terms \\( a_{n} \\) and \\( a_{n+1} \\) are the roots of the quadratic equation \\( x^{2} - 3nx + c_{n} = 0 \\) (for \\( n = 1, 2, 3, \\ldots \\)). Given that \\( a_{1} = 1 \\), find \\( c_{n} \\).\n\nPresent the answer in LaTex format: \\boxe... | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "5376",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5376 | [
{
"content": "What is the largest positive integer $n$ for which $n^3+200$ is divisible by $n-8$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 58 | [
{
"content": "Quadratic polynomial \\( P(x) \\) is such that \\( P(P(x)) = x^4 - 2x^3 + 4x^2 - 3x + 4 \\). What can be the value of \\( P(8) \\)? List all possible options.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\left[-\\frac{11}{4}, 0\\right]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \left[-\frac{11}{4}, 0\right] | [
{
"content": "Given the function $f(x) = |x + m| + |2x - 1|$ ($m \\in \\mathbb{R}$) \n(I) When $m = -1$, find the solution set of the inequality $f(x) \\leq 2$; \n(II) Let the solution set of the inequality $f(x) \\leq |2x + 1|$ be $A$, and $\\left[\\frac{3}{4}, 2\\right] \\subseteq A$, find the range of the ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\pi}{2}+2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\pi}{2}+2 | [
{
"content": "The function $f(x)=\\cos x+(x+1)\\sin x+1$ has the minimum and maximum values on the interval $\\left[0,2\\pi \\right]$. Find the critical points.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x^2 + (y-3)^2 = 1 \\text{ or } x^2 + (y-1)^2 = 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x^2 + (y-3)^2 = 1 \text{ or } x^2 + (y-1)^2 = 1 | [
{
"content": "The equation of a circle with its center on the y-axis, a radius of 1, and tangential to the line y = 2 is __________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "\\frac{14}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{14}{3} | [
{
"content": "Given that $$(x+y+z)(xy+xz+yz)=24$$ and $$x^2(y+z)+y^2(x+z)+z^2(x+y)=10$$ for real numbers $x$, $y$, and $z$, what is the value of $xyz$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2 < a < 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 < a < 3 | [
{
"content": "If the exponential function $y = (a - 2)^x$ is a decreasing function for $x \\in \\mathbb{R}$, determine the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "X = 1, Y = 100, Z = 10000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | X = 1, Y = 100, Z = 10000 | [
{
"content": "Koschei the Immortal poses three two-digit numbers: \\(a, b, c\\). Ivan Tsarevich must provide him with three numbers: \\(X, Y, Z\\), after which Koschei will tell him the sum \\(aX + bY + cZ\\). Tsarevich must determine the numbers \\(a, b,\\) and \\(c\\), or he will be beheaded. What numbers sho... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[\\frac{-π}{6},0]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [\frac{-π}{6},0] | [
{
"content": "The monotonically increasing interval of the function $f(x)=\\sin x-\\sqrt{3}\\cos x (x\\in[-π,0])$ is $\\boxed{\\text{answer}}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(-\\infty, -1) \\cup (1, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (-\infty, -1) \cup (1, +\infty) | [
{
"content": "Given $g(x) = |x-1| - |x-2|$, find the range of $g(x)$; if the solution set for the inequality $g(x) \\geq a^2 + a + 1$ ($x \\in \\mathbb{R}$) is empty, determine the range of values for the real number $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 6 | [
{
"content": "The \"Two Mice Through the Wall\" problem from the \"Nine Chapters on the Mathematical Art\" is a classic problem in Chinese mathematics: \"There is a wall of certain thickness. Two mice, one larger and one smaller, start to burrow through the wall from opposite sides. The larger mouse burrows 1 f... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x_{1}=\\frac{3}{2}, x_{2}=1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x_{1}=\frac{3}{2}, x_{2}=1 | [
{
"content": "Solve the equation: $2x^{2}-5x+3=0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 6 | [
{
"content": "Calculate: $\\left(\\frac{1}{8}\\right)^{-\\frac{2}{3}}+\\log_{3}9 =$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_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]... | math | {
"ground_truth": "0.727",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0.727 | [
{
"content": "Rounded to 3 decimal places, what is $\\frac{8}{11}$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
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