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_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": "302",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 302 | [
{
"content": "Given a $5 \\times 100$ grid with $n$ cells colored black and other cells colored white. Two cells are called \"neighbors\" if they share a common edge. Each cell can have at most two black neighbors. Find the maximum possible value of $n$.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 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{3}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{3}{2} | [
{
"content": "Given \\( a < -1 \\), the variable \\( x \\) satisfies \\( x^{2} + ax \\leq -x \\), and the minimum value of \\( x^{2} + ax \\) is \\( -\\frac{1}{2} \\). Find the value of \\( 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": "1511",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1511 | [
{
"content": "Let \\( a_{1}, a_{2}, \\cdots, a_{2014} \\) be a permutation of the positive integers \\( 1, 2, \\cdots, 2014 \\). Define\n\\[ S_{k} = a_{1} + a_{2} + \\cdots + a_{k} \\quad (k=1, 2, \\cdots, 2014). \\]\n\nWhat is the maximum number of odd numbers among \\( S_{1}, S_{2}, \\cdots, S_{2014} \\)?\n\n... | 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": "16",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 16 | [
{
"content": "Given the sequence ${a_n}$, the sum of the first n terms, S<sub>n</sub>, is equal to $n^2$. Find the value of $a_3^2 - a_2^2$.\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": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 | [
{
"content": "Given vectors $\\mathbf{a}$ and $\\mathbf{b}$ such that $\\|\\mathbf{a}\\| = 5,$ $\\|\\mathbf{b}\\| = 12,$ and $\\|\\mathbf{a} + \\mathbf{b}\\| = 13.$ Find $\\cos \\theta,$ where $\\theta$ is the angle between $\\mathbf{a}$ and $\\mathbf{b}.$\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 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": "38889",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 38889 | [
{
"content": "Let \\( f(n) \\) be the number of 0's in the decimal representation of the positive integer \\( n \\). For example, \\( f(10001123) = 3 \\) and \\( f(1234567) = 0 \\). Find the value of\n\\[ f(1) + f(2) + f(3) + \\ldots + f(99999) \\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 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": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 | [
{
"content": "Each principal of Jefferson Middle School serves exactly one 4-year term. Find the maximum number of principals this school could have during a 12-year period.\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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Determine the sum of the coordinates of the midpoint of the segment with endpoints $(8, -3)$ and $(-4, 15)$.\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}{15}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{14}{15} | [
{
"content": "Two lines intersect the $y$-axis at different points. The first line, with a $y$-intercept of 2, has a slope of 5 and an $x$-intercept $(u, 0)$. The second line, with a $y$-intercept of 3, has a slope of -7 and an $x$-intercept $(v, 0)$. What is the ratio of $u$ to $v$? Express your answer as a si... | 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": "\\lambda = 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \lambda = 1 | [
{
"content": "In triangle \\(ABC\\), points \\(C_{1}\\), \\(B_{1}\\), and \\(A_{1}\\) are located on sides \\(AB\\), \\(AC\\), and \\(CB\\), respectively, such that\n\n\\[ \\frac{AC_{1}}{C_{1}B} = \\frac{BA_{1}}{A_{1}C} = \\frac{CB_{1}}{B_{1}A} = \\lambda \\]\n\nLet the radii of the incircles of triangles \\(AC... | 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": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5 | [
{
"content": "Determine the value of \\( x \\) for which the expression \\( \\frac{x-5}{6x} \\) equals zero.\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{\\pi}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\pi}{4} | [
{
"content": "Given $\\tan\\beta= \\frac{1}{2}$, and $\\tan(\\alpha-\\beta)= \\frac{1}{3}$, where $\\alpha$ and $\\beta$ are acute angles, then $\\alpha= \\_\\_\\_\\_\\_\\_$.\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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 | [
{
"content": "Given $$f(x)= \\begin{cases} x^{2}, & \\text{if } x\\geq0 \\\\ -x, & \\text{if } x<0\\end{cases}$$, calculate $f[f(-2)]$.\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": "\\dfrac{3\\pi}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \dfrac{3\pi}{4} | [
{
"content": "In the Cartesian coordinate system, if the line $y=x$ is perpendicular to the line $\\begin{cases}x=1+\\cos \\theta \\\\ y=t\\sin \\theta\\end{cases}$, where $t$ is a parameter and $0 \\leqslant \\theta < \\pi$, find the value of $\\theta$.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 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": "131.35^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 131.35^\circ | [
{
"content": "Two forces, \\( P_{1} = 80 \\) dynes and \\( P_{2} = 130 \\) dynes, act on a body at two points that are \\( 12 \\) meters, \\( 3 \\) centimeters, and \\( 5 \\) millimeters apart. The direction of force \\( P_{1} \\) forms an angle of \\( 125^{\\circ} \\) with the line connecting the points of app... | 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": "Find the sum of all the integer solutions of the equation \\( x^4 - 49x^2 + 576 = 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": "\\log_5{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \log_5{2} | [
{
"content": "Given the function $f(x)$ satisfies $f(5^x) = x$, then $f(2) = \\ ?$\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": "a\\in\\left[\\frac{3}{4},1\\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | a\in\left[\frac{3}{4},1\right) | [
{
"content": "Given the function $f(x)=\\log_{a}(x^{3}-ax)$ where $a > 0$ and $a\\neq 1$, if the function $f(x)$ is monotonically increasing in the interval $\\left(-\\frac{1}{2},0\\right)$, then the range of values for the real number $a$ is _______.\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": "2400",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2400 | [
{
"content": "How many four-digit numbers greater than 3999 can be formed such that the product of the middle two digits exceeds 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": "\\text{For } n \\text{ divisible by 3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{For } n \text{ divisible by 3} | [
{
"content": "In each cell of an \\( n \\times n \\) table, an integer is written. It turned out that for all \\( k \\) from 1 to \\( n \\), the sum of the numbers in the \\( k \\)-th column is either one less or two more than the sum of the numbers in the \\( k \\)-th row. For which \\( n \\) is this possible?... | 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": "6^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 6^\circ | [
{
"content": "An equilateral triangle $ABC$ and a regular pentagon $BCDEF$ are coplanar, as shown. Determine the measure of angle $CAD$.\n\n[asy]\nsize(100);\npair B = dir(180);\npair C = dir(108);\npair D = dir(36);\npair E = dir(-36);\npair F = dir(-108);\npair A = extension(B, rotate(60, B)*C, C, rotate(60, ... | 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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3 | [
{
"content": "If $a$ and $b$ are opposite numbers, calculate the value of $a+b+3$.\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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Two frogs, A and B, are playing a jumping game. Frog A jumps 10 cm each time, and Frog B jumps 15 cm each time. They both jump once a second and start jumping from the same point. During the game, there are traps every 12 cm. When the first frog falls into a trap, the distance of the other frog fr... | 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": "\\text{f(x) is a decreasing function on } (-\\infty, 0)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{f(x) is a decreasing function on } (-\infty, 0) | [
{
"content": "Given an odd function $f(x)$ with the domain of $\\mathbb{R}$, which is a decreasing function on $[0, +\\infty)$, determine the monotonicity of $f(x)$ on $(-\\infty, 0)$ and provide a proof.\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": "Given sets $A=\\{x|4\\leq x<8\\}$, $B=\\{x|2<x<10\\}$, and $C=\\{x|x<a\\}$. \n(1) Find $A\\cup B$; $(\\mathbb{R}\\setminus A)\\cap B$; \n(2) If $A\\cap C\\neq \\emptyset$, find the range of $a$.\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{\\pi}{32}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\pi}{32} | [
{
"content": "A point $(x,y)$ is randomly picked from inside the rectangle with vertices $(0,0)$, $(2,0)$, $(2,2)$, and $(0,2)$. What is the probability that $x^2 + y^2 < y$?\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": "x(x-1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x(x-1) | [
{
"content": "Given $f(x)$ is an odd function, and when $x > 0$, $f(x) = -x(1+x)$, determine the expression for $f(x)$ when $x < 0$.\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": "19",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 19 | [
{
"content": "Ms. Johnson's fifth-grade class wants to participate in the annual four-person-team soccer tournament. The losing team of each match is eliminated from the tournament. If twenty teams compete, how many matches will be played to determine the winner?\n\nPresent the answer in LaTex format: \\boxed{Y... | 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": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Given the set $A=\\{1,2,3\\}$, $B=\\{(x,y)|x\\in A, y\\in A, x+y\\in A\\}$, calculate the number of subsets of set $B$.\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\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2\sqrt{2} | [
{
"content": "A coordinate system and parametric equations (4-4)\n\nGiven that the polar coordinate equation of circle $E$ is $ρ=4\\sin θ$, establish a planar rectangular coordinate system with the pole as the origin and the positive half of the polar axis as the $x$-axis, using the same unit length (where $(ρ,... | 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": "-59.62^\\circ, \\quad -35.17^\\circ, \\quad 0.956^\\circ, \\quad 35.36^\\circ, \\quad 60.39^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -59.62^\circ, \quad -35.17^\circ, \quad 0.956^\circ, \quad 35.36^\circ, \quad 60.39^\circ | [
{
"content": "We need to find the approximate values of the roots for the equation\n\n$$\n\\operatorname{tg} x + \\operatorname{tg} 2x + \\operatorname{tg} 3x = 0.1\n$$\n\nFirst, determine the roots of the equation\n\n$$\n\\operatorname{tg} x + \\operatorname{tg} 2x + \\operatorname{tg} 3x = 0\n$$\n\nand then, ... | 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": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 7 | [
{
"content": "Determine the value of $k$ for which the equation $\\frac{x-3}{x-4} = \\frac{x-k}{x-8}$ has no solution.\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": "664",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 664 | [
{
"content": "If\n\\[1 \\cdot 1990 + 2 \\cdot 1989 + 3 \\cdot 1988 + \\dots + 1989 \\cdot 2 + 1990 \\cdot 1 = 1990 \\cdot 995 \\cdot y,\\]\ncompute the integer \\(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": "500",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 500 | [
{
"content": "\nLet \\( \\mathbb{N} \\) be the set of all positive integers. For a subset \\( S \\) of \\( \\mathbb{N} \\) and \\( n \\in \\mathbb{N} \\), define\n$$\nS \\oplus \\{n\\} = \\{ s + n \\mid s \\in S \\}.\n$$\n\nAdditionally, define the subset \\( S_k \\) as follows:\n$$\nS_1 = \\{1\\}, \\quad S_k =... | 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{align*}\n\\sin 30^\\circ &= \\frac{1}{2}, & \\cos 30^\\circ &= \\frac{\\sqrt{3}}{2}, & \\tan 30^\\circ &= \\frac{\\sqrt{3}}{3}\\\\\n\\sin 45^\\circ &= \\frac{\\sqrt{2}}{2}, & \\cos 45^\\circ &= \\frac{\\sqrt{2}}{2}, & \\tan 45^\\circ &= 1\\\\\n\\sin 60^\\circ &= \\frac{\\sqrt{3}}{2}, & \\co... | {
"index": 0,
"split": "dummy"
} | \begin{align*}
\sin 30^\circ &= \frac{1}{2}, & \cos 30^\circ &= \frac{\sqrt{3}}{2}, & \tan 30^\circ &= \frac{\sqrt{3}}{3}\\
\sin 45^\circ &= \frac{\sqrt{2}}{2}, & \cos 45^\circ &= \frac{\sqrt{2}}{2}, & \tan 45^\circ &= 1\\
\sin 60^\circ &= \frac{\sqrt{3}}{2}, & \cos 60^\circ &= \frac{1}{2}, & \tan 60^\circ &= \sqrt{3}\... | [
{
"content": "What are the sines, cosines, and tangents of the angles $30^{\\circ}, 45^{\\circ}, 60^{\\circ}, 90^{\\circ}$?\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": "10\\sqrt{3} \\text{ feet (width)}, 20\\sqrt{3} \\text{ feet (length)}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 10\sqrt{3} \text{ feet (width)}, 20\sqrt{3} \text{ feet (length)} | [
{
"content": "Luke wants to fence a rectangular piece of land of exactly 600 square feet to create a rectangular garden. He wants the length of the garden to be twice its width. What dimensions should the garden have to use the exact amount of space and the least fencing?\n\nPresent the answer in LaTex format: ... | 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": "Parallelogram $EFGH$ has vertices $E(5,4)$, $F(-1,-4)$, $G(-7,-2)$, and $H(1,6)$. If a point is selected at random from the region determined by the parallelogram, what is the probability that the point is not above the $x$-axis? Express your answer as a common fraction.\n\nPresent the answer in L... | 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": "30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 30 | [
{
"content": "What is the largest quotient that can be formed using two numbers chosen from the set $\\{ -30, -5, -1, 0, 2, 10, 15 \\}$?\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 - \\frac{\\pi^2}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 - \frac{\pi^2}{4} | [
{
"content": "Given the function $f(x)= \\sqrt{3}\\sin(\\pi-x)\\cos(-x)+\\sin(\\pi+x)\\cos\\left(\\frac{\\pi}{2}-x\\right)$, a lowest point on its graph is $A$, and the two nearest highest points are $B$ and $C$, respectively. Calculate the dot product $\\vec{AB} \\cdot \\vec{AC}$.\n\nPresent the answer in LaTe... | 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": "41",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 41 | [
{
"content": "From 9 students, select 5 to form a class committee. The selection must meet the following conditions: both of students A and B must be either selected together or not selected together, and students C and D must not be selected together. How many possible selections are there? (Answer in numerica... | 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 > -4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | a > -4 | [
{
"content": "Let the universal set \\\\(U=\\mathbb{R}\\\\), and the sets \\\\(A=\\{ x|-1\\leqslant x < 3 \\}\\\\), \\\\(B=\\{ x|2x-4\\geqslant x-2 \\}\\\\)\n\n\\\\((1)\\\\) Find \\\\({{C}_{U}}(A\\cap B)\\\\);\n\n\\\\((2)\\\\) If the set \\\\(C=\\{x|2x+a > 0\\}\\\\) satisfies \\\\(B\\cup C=C\\\\), find the rang... | 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-\\dfrac{\\pi}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1-\dfrac{\pi}{8} | [
{
"content": "In a square $ABCD$ with side length $4$, find the probability that $\\angle AMB$ is an acute angle.\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{9}{10}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{9}{10} | [
{
"content": "A real number \\(x\\) is chosen uniformly at random from the interval \\([0, 1000]\\). Find the probability that\n\\[ \n\\left\\lfloor\\frac{\\left\\lfloor\\frac{x}{2.5}\\right\\rfloor}{2.5}\\right\\rfloor = \\left\\lfloor\\frac{x}{6.25}\\right\\rfloor.\n\\]\n\nPresent the answer in LaTex format: ... | 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": "Let \\( g : \\mathbb{R} \\to \\mathbb{R} \\) be a function such that\n\\[ g(xg(y) - x) = xy - g(x) \\] for all \\( x, y \\).\n\nLet \\( m \\) be the number of possible values of \\( g(3) \\), and let \\( t \\) be the sum of all possible values of \\( g(3) \\). Find \\( m \\times t \\).\n\nPresent ... | 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{1}{2} s(2-\\sqrt{3})",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{2} s(2-\sqrt{3}) | [
{
"content": "Given square ABCD with side s, quarter-circle arcs with radii s and centers at A and B are drawn. These arcs intersect at a point X inside the square. What is the distance from X to the side of CD?\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": "\\min\\{p, k+l-1\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \min\{p, k+l-1\} | [
{
"content": "Let \\( p \\) be a prime number. Given that the integers \\( x_{1}, x_{2}, \\cdots, x_{k} \\) are pairwise distinct modulo \\( p \\), and the integers \\( y_{1}, y_{2}, \\cdots, y_{l} \\) are pairwise distinct modulo \\( p \\), then the sums \n\\[ x_{i} + y_{j} \\quad (1 \\leqslant i \\leqslant k,... | 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": "32",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 32 | [
{
"content": "Evaluate $64^{5/6}$.\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": "\\text{The range for } m \\text{ is } (-\\infty, 4]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{The range for } m \text{ is } (-\infty, 4] | [
{
"content": "Given the universal set $U=\\mathbb{R}$, and the sets $A=\\{x \\mid -7 \\leq 2x-1 \\leq 7\\}$ and $B=\\{x \\mid m-1 \\leq x \\leq 3m-2\\}$. If $A \\cap B = B$, find the range of the real number $m$.\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{4}{9}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{4}{9} | [
{
"content": "Express as a common fraction: $0.\\overline{6} + 0.\\overline{2} - 0.\\overline{4}$.\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": "20",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 20 | [
{
"content": "In a rectangular parallelepiped \\(ABCDA_1B_1C_1D_1\\), the lengths of the edges are given as \\(AB=60\\), \\(AD=30\\), and \\(AA_1=15\\). Point \\(E\\) is marked at the midpoint of edge \\(A_1B_1\\), and point \\(F\\) is marked at the midpoint of edge \\(B_1C_1\\). Find the distance between the l... | 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,e]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (0,e] | [
{
"content": "Let the set $M=\\{x|2^{x+1} > 1\\}$, and $N=\\{x|\\ln x \\leqslant 1\\}$. Find the intersection $M \\cap N$.\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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "Given the parabola \\\\(E\\\\): \\\\(y^{2}=4x\\\\) with focus \\\\(F\\\\), a line \\\\(l\\\\) passing through point \\\\(F\\\\) intersects the parabola at points \\\\(A\\\\) and \\\\(B\\\\), and intersects the \\\\(y\\\\)-axis at point \\\\(C\\\\). Let \\\\(O\\\\) be the origin of the coordinates.... | 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": "2052",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2052 | [
{
"content": "Given that $x$ is the arithmetic square root of $16$, and $y$ is the square root of $9$, find the value of $x^{2}+y^{2}+x+2023$.\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": "0.79 \\text{m}^3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0.79 \text{m}^3 | [
{
"content": "The height of a right frustum of a cone is $m=\\frac{3}{\\pi} \\mathrm{dm}$, and the inclination angle of the slant height is $\\alpha=43^{\\circ} 40^{\\prime} 42.2^{\\prime \\prime}$. What is the volume of this frustum if the volume of the complete cone is $k=1 \\mathrm{~m}^{3}$?\n\nPresent the a... | 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} = 2 + \\sqrt{11}, x_{2} = 2 - \\sqrt{11}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x_{1} = 2 + \sqrt{11}, x_{2} = 2 - \sqrt{11} | [
{
"content": "Solve the equation: $x^{2}-4x-7=0$.\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, 2]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [-1, 2] | [
{
"content": "Given the function $f(x) = (2\\sqrt{3}\\cos \\omega x + \\sin \\omega x)\\sin \\omega x - \\sin^2(\\frac{\\pi}{2} + \\omega x), (\\omega > 0)$, and the distance from one symmetry center of the graph of the function $y=f(x)$ to the nearest symmetry axis is $\\frac{\\pi}{4}$.\n\n1. Find the interval... | 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) 18",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | B) 18 | [
{
"content": "Let $Q$ be the quadrilateral in the coordinate plane with vertices at $(0,0), (6,0), (6,4),$ and $(0,4)$. Consider the following six isometries (rigid transformations) of the plane: rotations of $90^{\\circ}, 180^{\\circ},$ and $270^{\\circ}$ counterclockwise around the origin, reflection across t... | 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": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Calculate: \n(1) $2\\log_{3}2-\\log_{3}\\frac{32}{9}+\\log_{3}8-5^{log_{5}3}$ \n(2) $\\log_{2}25 \\cdot \\log_{3}4 \\cdot \\log_{5}9$\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{\\sqrt{5}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\sqrt{5}}{3} | [
{
"content": "Given $\\alpha \\in \\left(0,\\pi \\right)$, and $3\\cos 2\\alpha -8\\cos \\alpha =5$, find $\\sin \\alpha$.\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": "\\text{The given equation } \\frac{3}{x} + \\frac{2}{y} = \\frac{1}{3} \\text{ is equivalent to } \\frac{3y}{y - 6} = x.",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{The given equation } \frac{3}{x} + \frac{2}{y} = \frac{1}{3} \text{ is equivalent to } \frac{3y}{y - 6} = x. | [
{
"content": "If $x \\neq 0$ or $3$ and $y \\neq 0$ or $5$, then $\\frac{3}{x} + \\frac{2}{y} = \\frac{1}{3}$, solve for an equivalent equation.\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": "(-\\infty, 2] \\cup [4, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (-\infty, 2] \cup [4, +\infty) | [
{
"content": "The solution set of the inequality \\( |x-3| + |x-a| < 1 \\) is empty. Determine the range of 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": "19",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 19 | [
{
"content": "Given $x+y=5$ and $xy=3$, calculate the value of $x^{2}+y^{2}$.\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": "\\frac{x^{2}}{2}-\\frac{y^{2}}{3}=1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{x^{2}}{2}-\frac{y^{2}}{3}=1 | [
{
"content": "Given the hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ with an eccentricity of $\\frac{\\sqrt{10}}{2}$, and it passes through the point $(2, \\sqrt{3})$, find the standard equation of the hyperbola.\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{1}{e}, 0)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (-\frac{1}{e}, 0) | [
{
"content": "Given the function $f(x)=\\ln x-\\frac{m}{x}$ has a local minimum less than $0$, the range of real number $m$ 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": "-28",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -28 | [
{
"content": "Find the sum of all integral values of \\( c \\) with \\( c \\leq 30 \\) for which the equation \\( y = x^2 - 9x - c \\) has two rational roots.\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": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5 | [
{
"content": "A clothing store has a special offer on sweaters. Promotion X says, \"Buy one sweater at full price and get the second sweater at 40% off.\" Promotion Y says, \"Buy one sweater and get $15 off the second sweater.\" Michael wants to buy two sweaters, each originally costing $50. He can only use one... | 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\\sqrt{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4\sqrt{3} | [
{
"content": "In triangle $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively, with $b=4$ and $\\frac{\\cos B}{\\cos C} = \\frac{4}{2a - c}$.\n(1) Find the measure of angle $B$;\n(2) Find the maximum area of $\\triangle ABC$.\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": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "Determine the number of pairs $(x, y)$ such that $12, x, y, xy$ form an arithmetic progression.\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": "25",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 25 | [
{
"content": "Marsha has three numbers, $a$, $b$, and $c$. When she divides $a$ by 80 she gets a remainder of 75. When she divides $b$ by 120 she gets a remainder of 115. She also has $c$ which when divided by 160 gives a remainder of 155. What remainder does she get when she divides $a+b+c$ by 40?\n\nPresent t... | 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": "72",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 72 | [
{
"content": "19. If \\( a_{1}, a_{2}, \\cdots, a_{m} \\) is an arithmetic sequence with both the first term and the common difference being positive integers, and none of the terms contains the digit 9 in their decimal representation, find the maximum value of the number of terms \\( m \\).\n\nPresent the 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": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Let $U=\\frac{1}{4-\\sqrt{9}}+\\frac{1}{\\sqrt{9}-\\sqrt{8}}-\\frac{1}{\\sqrt{8}-\\sqrt{7}}+\\frac{1}{\\sqrt{7}-\\sqrt{6}}-\\frac{1}{\\sqrt{6}-3}$, evaluate the value of $U$.\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 + i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 + i | [
{
"content": "Evaluate $i^{12} + i^{17} + i^{22} + i^{27} + i^{32} + i^{37}$.\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": "182",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 182 | [
{
"content": "How many numbers from $1$ to $200$ are neither perfect squares nor perfect cubes?\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": "72",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 72 | [
{
"content": "The numbers \\(1, 2, \\ldots, 9\\) are placed in a \\(3 \\times 3\\) square. We will call such arrangements \"feng shui\" if for any choice of three cells, located in different columns and different rows, the sum of the numbers in the chosen cells is equal to 15. Find the number of all \"feng shui... | 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": "23",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 23 | [
{
"content": "Let the function $f(x) = \\left\\lfloor x \\right\\rfloor\\{x\\}$ . Compute the smallest positive integer $n$ such that the graph of $f(f(f(x)))$ on the interval $[0,n]$ is the union of 2017 or more line segments.\n\n*Proposed by Ayush Kamat*\n\nPresent the answer in LaTex format: \\boxed{Y... | 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}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{9}{4} | [
{
"content": "Given the function $f\\left(x\\right)=\\sqrt{\\left|x+1\\right|+\\left|x-3\\right|-m}$ with a domain of $R$.\n\n(1) Find the range of real number values for $m$.\n(2) If the maximum value of $m$ is $n$, and positive numbers $a$ and $b$ satisfy $\\frac{2}{3a+b}+\\frac{1}{a+2b}=n$, find the minimum ... | 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": "x^{11}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x^{11} | [
{
"content": "Simplify \\(x^5 \\cdot x^6\\).\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 a complex number $z=\\frac{1-i}{{i}^{3}}$, find the imaginary part of $\\overline{z}$.\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": "20",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 20 | [
{
"content": "How many distinct triangles can be constructed by connecting three different vertices of a regular octahedron? (Two triangles are distinct if they have different locations in space.)\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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3 | [
{
"content": "In the geometric sequence $\\{a_n\\}$, $a_1=4$, and the common ratio is $q$. The sum of the first $n$ terms is $S_n$. If the sequence $\\{S_n+2\\}$ is also a geometric sequence, then $q=\\boxed{3}$.\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": "\\frac{15}{451}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{15}{451} | [
{
"content": "Define $a@b = ab - b^{2}$ and $a\\#b = a + b - ab^2 + a^3$. Simplify the expression $\\frac{8@3}{8\\#3}$.\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": "-20",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -20 | [
{
"content": "What value of \\( x \\) will give the minimum value of \\( 3x^2 - 18x + 7 \\)?\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)^3 \\cdot C_5^2 = -640",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (-4)^3 \cdot C_5^2 = -640 | [
{
"content": "Given that $a=-2 \\int_{0}^{π} \\sin x dx$, find the coefficient of $x$ in the expansion of the binomial $(x^2 + \\frac{a}{x})^5$.\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": "a>2 \\text{ or } a<-2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | a>2 \text{ or } a<-2 | [
{
"content": "Given proposition p: The equation $2x^2+ax-a^2=0$ has a solution in the interval $[-1,1]$; proposition q: There is only one real number $x$ that satisfies the inequality $x^2+2ax+2a\\leq0$. If the proposition “$p \\lor q$” is false, find the range of values for $a$.\n\nPresent the answer in LaTex ... | 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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x=1 | [
{
"content": "Solve the equation \\( 2021 \\cdot \\sqrt[202]{x^{2020}} - 1 = 2020x \\) for \\( x \\geq 0 \\). (10 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": "24",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 24 | [
{
"content": "Given the arithmetic sequence $\\{a_n\\}$, $S_{10} = 120$, calculate the value of $a_2 + a_9$.\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": "(-1)^n pq + 1 \\text{ or } -pq - 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (-1)^n pq + 1 \text{ or } -pq - 1 | [
{
"content": "Let \\( p \\) and \\( q \\) be distinct prime numbers, and let \\( n \\geq 3 \\) be a positive integer. Find all integers \\( a \\) such that the polynomial \\( f(x) = x^n + ax^{n-1} + pq \\) can be factored into a product of two non-constant polynomials with integer coefficients.\n\nPresent the a... | 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": "T_n = (n - 1) \\cdot 3^{n+1} + 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | T_n = (n - 1) \cdot 3^{n+1} + 3 | [
{
"content": "Given a positive geometric sequence $\\{a_n\\}$ that satisfies $a_{2n+1} = 3 \\cdot 9^n$,\n\n(1) Find the general term formula for the sequence $\\{a_n\\}$;\n\n(2) Let $b_n = (2n - 1)a_n$, find the sum of the first $n$ terms of the sequence $\\{b_n\\}$, denoted as $T_n$.\n\nPresent the answer in L... | 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, \\frac{9}{5})",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [-3, \frac{9}{5}) | [
{
"content": "If the solution set of the inequality $(a^{2}-9)x^{2}+\\left(a+3\\right)x-1\\geqslant 0$ is an empty set, determine the range of the real number $a$.\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": "\\{1, 2, \\ldots, n\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \{1, 2, \ldots, n\} | [
{
"content": "Determine all nonempty finite sets \\( S=\\{a_{1}, \\ldots, a_{n}\\} \\) of \\( n \\) distinct positive integers such that \\( a_{1} \\cdots a_{n} \\) divides \\((x+a_{1}) \\cdots (x+a_{n})\\) for every positive integer \\( x \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 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": "33600",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 33600 | [
{
"content": "How many six-digit numbers with all distinct digits can be formed? Among these numbers, how many have exactly four odd digits?\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} \\leq a < \\frac{1}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{4} \leq a < \frac{1}{3} | [
{
"content": "Given that the odd function $f(x)$ is a decreasing function on the domain $[-2, 2]$, if $f(2a+1) + f(4a-3) > 0$, find the range of 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": "0 \\text{ or } 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 \text{ or } 3 | [
{
"content": "Let the function $f(x)=\\begin{cases} \nx+3, & x\\leq 0 \\\\\nx^2-2x, & x > 0\n\\end{cases}$. If $f(m)=3$, then the real number $m=$ ______________.\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": "475",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 475 | [
{
"content": "A company has a fixed cost of 0.5 ten thousand yuan for producing a type of machine. However, for every 100 units produced, an additional variable cost of 0.25 ten thousand yuan is incurred. The annual demand for this product in the market is 500 units, and the revenue function (in ten thousand yu... | 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": "Acute-angled triangle $\\triangle ABC$ is inscribed in a circle with center at $O$; $\\stackrel \\frown {AB} = 150^\\circ$ and $\\stackrel \\frown {BC} = 60^\\circ$.\nA point $E$ is chosen on the minor arc $AC$ of the circle such that $OE$ is perpendicular to $AC$. Determine the ratio of the magni... | 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": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 | [
{
"content": "Given that each of the $20$ balls is tossed independently and at random into one of the $5$ bins, find the ratio of the probability that some bin ends up with $3$ balls, another with $5$ balls, and the other three with $4$ balls each, to the probability that every bin ends up with $4$ balls.\n\nPr... | 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": "[0,1+ \\frac { \\sqrt {3}}{2}]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [0,1+ \frac { \sqrt {3}}{2}] | [
{
"content": "Given the function $f(x)=2\\sin x\\sin (x+ \\frac {π}{6})$.\n(1) Find the smallest positive period and the monotonically increasing interval of the function $f(x)$;\n(2) Find the range of $f(x)$ when $x\\in[0, \\frac {π}{2}]$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 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{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{1}{2} | [
{
"content": "Given complex numbers \\( z_{1}, z_{2}, z_{3} \\) with arguments \\( \\alpha, \\beta, \\gamma \\) respectively, and magnitudes \\( \\left|z_{1}\\right| = 1, \\left|z_{2}\\right| = k, \\left|z_{3}\\right| = 2 - k \\) such that \\( z_{1} + z_{2} + z_{3} = 0 \\):\n\n1. Find the value of \\( k \\) for... | 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{3d - 3}{5d - 4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{3d - 3}{5d - 4} | [
{
"content": "Let $c$ and $d$ be real numbers such that\n\\[\\frac{c}{d} + \\frac{c}{d^2} + \\frac{c}{d^3} + \\dots = 3.\\]Find\n\\[\\frac{c}{c + 2d} + \\frac{c}{(c + 2d)^2} + \\frac{c}{(c + 2d)^3} + \\dotsb.\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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": "7350",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 7350 | [
{
"content": "The smallest positive integer $x$ for which $1260x=N^3$, where $N$ is an integer, find the value of $x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.