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values | ground_truth_solution stringclasses 177
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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nThe points in a plane are colored in such a way that each point is either red or blue.\n\n(i) Show that for any real number $x$, there exists a color such that we can find two points of that color that are at a distance of $x$ from e... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given the array of integers nums, you will choose two different indices i and j of that array. Return the maximum value of (nums[i]-1)*(nums[... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that circles $C_{1}$ and $C_{2}$ intersect at two points, one of which has coordinates $(9,6)$, and the product of their radii is 68. If the $x$-axis and the line $y = mx$ (where \\(m > 0\\)) are both tangent to the two circles, ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Yukihira is counting the minimum number of lines $m$ , that can be drawn on the plane so that they intersect in exactly $200$ distinct points.What is $m$ ?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAl... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $a$ be a positive constant. Find the value of $\\ln a$ such that \n\\[\\frac{\\int_1^e \\ln (ax)\\ dx}{\\int_1^e x\\ dx}=\\int_1^e \\frac{\\ln (ax)}{x}\\ dx.\\]"
},
{
"from": "assistant",
"value": "<|begin_of_though... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. S is the set \\(\\{x \\in \\mathbb{R} \\;|\\; x^4 - 13x^2 + 36 \\leq 0\\}\\). Find the maximum value of \\(f(x) = x^3 - 3x\\) on S."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the ma... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nThe circle inscribed in a right-angled triangle with legs of lengths 6 and 8 touches the hypotenuse at point \\( M \\). Find the distance from point \\( M \\) to the vertex of the right angle."
},
{
"from": "assistant",
"... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The function \\( f(x) \\) has a derivative of 0 at \\( x = x_0 \\), but it is not necessarily an extremum point. Such a function can be (only one example is needed)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that a circle intersects a conic section at four points, in order $A, B, C, D$, prove that the angles between the common chords $AC$ and $BD$ and the axis of symmetry are complementary."
},
{
"from": "assistant",
"val... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Where would people go after they pick some food to buy in a store?\nA: apartment\nB: bus depot\nC: neighbor's house\nD: restroom\nE: end of line"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out this question. So the question ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that \\( m, n \\in \\mathbf{Z} \\), and \\( 1 \\leq m \\leq 99 \\), \\( 1 \\leq n \\leq 99 \\), the number of ordered pairs \\((m, n)\\) such that \\((m+n)^{2} + 3m + n\\) is a perfect square is ( ):\n\nA. 98\n\nB. 100\n\nC. 96\n... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \\[ 8.414 \\cos x + \\sqrt{\\frac{3}{2} - \\cos^2 x} - \\cos x \\cdot \\sqrt{\\frac{3}{2} - \\cos^2 x} = 1 \\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, let's tackle this equation step by step. T... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "What is the expected effect of black holes on the cosmic neutrino background? Specifically, how does the presence of black holes affect the energy spectrum and number density of cosmic neutrinos observed on Earth? Consider different types and sizes of black holes, as well as thei... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( n \\in \\mathbf{Z} \\), and the function \\( f: \\mathbf{Z} \\rightarrow \\mathbf{R} \\) satisfies\n\nProve: For any \\( n \\leq 100 \\), \\( f(n) = 91 \\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19.$ Point $P$ is on segment $AB$ with $AP = 6$, and $Q$ is on segment $CD$ with $CQ = 7$. The line through $P$ and $Q$ intersects the circle at $X$ and $Y$... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.“The Drinking Musicians”, a widely known and popular folk group, are coming to your town. The musici... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A rectangle with area $n$ with $n$ positive integer, can be divided in $n$ squares(this squares are equal) and the rectangle also can be divided in $n + 98$ squares (the squares are equal). Find the sides of this rectangle"
}... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In an isosceles triangle \\( ABC \\) with base \\( AC \\) and the angle at vertex \\( B \\) equal to \\( 36^\\circ \\), a bisector \\( AD \\) is drawn.\n\nProve that the triangles \\( CDA \\) and \\( ADB \\) are isosceles."
},
{
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The function \\( y = a^{2x} + 2a^x - 1 \\) (where \\( a > 0 \\) and \\( a \\neq 1 \\)) has a maximum value of 14 on the interval \\([-1, 1]\\). The value of \\( a \\) is \\(\\qquad\\)."
},
{
"from": "assistant",
"value": "<... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the integer \\( n \\geqslant 2 \\),\n\\[ A_{n}=\\sum_{k=1}^{n} \\frac{3 k}{1+k^{2}+k^{4}}, \\quad B_{n}=\\prod_{k=2}^{n} \\frac{k^{3}+1}{k^{3}-1} \\]\n\ndetermine the relationship between \\( A_{n} \\) and \\( B_{n} \\)."
},
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( f(x) \\) be a cubic polynomial, and \\( r_1, r_2, r_3 \\) be the roots of \\( f(x) \\). If \\(\\frac{f\\left(\\frac{1}{2}\\right) + f\\left(-\\frac{1}{2}\\right)}{f(0)} = 1003\\), find the value of \\(\\frac{1}{r_1 r_2} + \\fra... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $p$ be a prime number. Prove that\n\n$1^{0} .\\binom{p-1}{k}^{2}-1$ is divisible by $p$,\n\n$2^{0} .\\binom{p-1}{0}^{s}+\\binom{p-1}{1}^{s}+\\binom{p-1}{2}^{s}+\\cdots+\\binom{p-1}{p-1}^{s}$ is divisible by $p$ if $s$ is even, but ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Natasha and Inna bought identical boxes of tea bags. It is known that one tea bag is enough for either two or three cups of tea. Natasha's box lasted for 41 cups of tea, while Inna's box lasted for 58 cups. How many tea bags were in th... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $ABC$ be an equilateral triangle. From the vertex $A$ we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray reaches a side, it then bounces off following the law... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Four identical isosceles trapezoids are placed such that their lower bases form the two diagonals of a square. If $PX = 3XQ$, find the ratio of the area of the shaded regions to the area of the entire square."
},
{
"from": "ass... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( ABCD \\) be a trapezoid with sides \\( AD \\) and \\( BC \\) parallel and whose diagonals intersect at point \\( P \\). The point \\( Q \\) is between the lines \\( (AD) \\) and \\( (BC) \\) such that \\( \\angle AQD = \\angle ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $S$ be the set of points on two rays that intersect at an angle of $120^{\\circ}$. $P$ is a fixed point on the angle bisector of these two rays and inside the angle. Consider all distinct equilateral $\\triangle PQR$, where $Q$ and... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Vasya wrote a true statement:\n\n\"In this sentence, $1 / 3$ of all digits are the digit 3, and $1 / 2$ of all digits are the digit $1$.\"\n\nBut Kolya wrote the following sentence:\n\n\"In this sentence, 1/... of all digits are the di... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For a given number N, find whether it is a factorial number or not. A Factorial number is a number w... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two players are playing \"tic-tac-toe\" on an infinite sheet of graph paper. The starter places a cross in any cell. On each of their subsequent moves, they must place a cross in a free cell adjacent to one of the cells where a cross i... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Read problems statements in mandarin chinese, russian and vietnamese as well. \n\nYou are given a mu... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given a row of n coins of values arr[1], arr[2], ... arr[n], where n is even. Geek plays a game agai... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $\\{a_k\\}$ be a sequence of integers such that $a_1=1$ and $a_{m+n}=a_m+a_n+mn,$ for all positive integers $m$ and $n.$ Find $a_{12}.$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to fin... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a circle with a radius of 4 cut out of cardboard, a ruler, and a compass, construct a rectangle on a sheet of paper that has the same area as the circle."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOk... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Evaluate $i^{22} + i^{222}$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to evaluate i²² plus i²²². Hmm, let me start by recalling what the powers of i are. I remember that the imaginary uni... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string $S$, which is balanced parentheses with a star symbol '*' inserted.\n\nAny ba... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a tetrahedron \\(ABCD\\), points \\(A_i, B_i, C_i, D_i\\) are taken in the planes defining its faces such that the lines \\(AA_i, BB_i, CC_i, DD_i\\) are parallel to each other. Find the ratio of the volumes of tetrahedrons \\(AB... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Consider the points \\( P(0,0) \\), \\( Q(4,0) \\), and \\( R(1,2) \\). The line with equation \\( y = mx + b \\) is parallel to \\( PR \\) and passes through the midpoint of \\( QR \\). What is the value of \\( b \\)?"
},
{
"f... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given an array of numbers (in string format), you must return a string. The numbers correspond to the letters of the alphabet in reverse orde... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We have a string S consisting of uppercase English letters. Additionally, an integer N will be given... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the sum of all primes \\( p \\) for which there exists a prime \\( q \\) such that \\( p^{2} + p q + q^{2} \\) is a square."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the sum o... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Karl likes Codeforces and subsequences. He wants to find a string of lowercase English letters that ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. There is a plate of fruits. When counted in groups of 3, there are 2 left over; when counted in groups of 4, there are 3 left over; when counted in groups of 5, there are 4 left over; and when counted in groups of 6, there are 5 left o... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the flux of the vector field \\(\\mathbf{a} = y^2 \\mathbf{j} + z \\mathbf{k}\\) through the part of the surface \\(z = x^2 + y^2\\), cut off by the plane \\(z=2\\). The normal vector is taken to be outward with respect to the reg... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nFor how many natural numbers \\( n \\) not exceeding 600 are the triples of numbers\n\n\\[ \\left\\lfloor \\frac{n}{2} \\right\\rfloor, \\left\\lfloor \\frac{n}{3} \\right\\rfloor, \\left\\lfloor \\frac{n}{5} \\right\\rfloor \\quad\\... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "When helping soldiers in the middle of fighting, where do medics practice practice their craft?\nA: funeral\nB: battlefield\nC: hospital\nD: war\nE: safety tent"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this question. The question... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the function \\( f(x) = ax^2 + bx + c \\) where \\( a, b, c \\in \\mathbb{R} \\) and it satisfies \\( \\max_{x \\in [0,1]} |f(x)| \\leq 1 \\), find the maximum possible value of \\( \\max_{x \\in [0,1]} |g(x)| \\) for the functio... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Vus the Cossack has a simple graph with n vertices and m edges. Let d_i be a degree of the i-th vert... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Determine all integers \\( n > 3 \\) for which there exist \\( n \\) points \\( A_{1}, A_{2}, \\cdots, A_{n} \\) in the plane, and real numbers \\( r_{1}, r_{2}, \\cdots, r_{n} \\) such that:\n(1) Any three points among \\( A_{1}, A_{2... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Read problems statements in Mandarin, Russian and Vietnamese as well. \n\nThere are N sets of intege... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Calculate the definite integral:\n\n$$\n\\int_{0}^{1}(x+1) \\cdot \\ln ^{2}(x+1) \\, dx\n$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to calculate the definite integral of (x + 1) times th... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Suppose medians \\( m_{a} \\) and \\( m_{b} \\) of a triangle are orthogonal. Prove that:\n(a) The medians of that triangle correspond to the sides of a right-angled triangle.\n(b) The inequality \n\\[ 5\\left(a^{2}+b^{2}-c^{2}\\right)... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "How does the presence of antigens trigger the immune response and what are the specific steps involved in the response of the immune system to combat the antigen?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how the presen... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In triangle \\(ABC\\), the excircle opposite side \\(AC\\) touches the extensions of sides \\(BC\\), \\(AC\\), and \\(AB\\) at points \\(A_1\\), \\(B_1\\), and \\(C_1\\) respectively. Let \\(F\\) be the midpoint of segment \\(A_1B_1\\)... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let the set consisting of the squares of the positive integers be called $u$; thus $u$ is the set $1, 4, 9, 16 \\ldots$. \nIf a certain operation on one or more members of the set always yields a member of the set, \nwe say that the se... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $p$ and $q$ be two real numbers such that the quadratic equation $x^{2}+px+q=0$ has two distinct real roots $u$ and $v$ (with $u > v$). The coefficients $p$ and $q$ are slightly modified by less than 0.01, and it is assumed that th... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the pairs of positive integers \\((a, b)\\) such that \\(\\frac{a b^{2}}{a+b}\\) is a prime number, where \\(a \\neq b\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find al... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Chef Jessie has a lot of recipes with her (N). She often remembered the starting few characters of t... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. There are 9 points $A_{1}, A_{2}, \\cdots, A_{9}$ on a plane, with no three points being collinear. Prove that there exists a convex pentagon among them."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nCalculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\sin ^{6} x \\cos ^{2} x \\, dx\n$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to calculate the definite integral fr... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Four standard, six-sided dice are to be rolled. If the product of their values turns out to be an even number, what is the probability their sum is odd? Express your answer as a common fraction."
},
{
"from": "assistant",
"... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Show that \\( K_4 \\) is planar, but \\( K_{3,3} \\) and \\( K_5 \\) are not."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to show that the complete graph K₄ is planar, but the complete bipar... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nIn a room, there are several children and a pile of 2021 candies. Each child takes turns approaching the pile, divides the number of candies by the number of children in the room (including themselves), rounds (if the result is not a... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two concentric circles have radii $1$ and $4$ . Six congruent circles form a ring where each of the six circles is tangent to the two circles adjacent to it as shown. The three lightly shaded circles are internally tangent to the ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. For what is the smallest \\( n \\) such that there exist \\( n \\) numbers within the interval \\((-1, 1)\\), whose sum is 0 and the sum of their squares is 40?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nO... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In triangle $ABC$, the angle bisectors $AA_{1}$ and $BB_{1}$ intersect at point $O$. Find the ratio $AA_{1} : OA_{1}$ given $AB=6, BC=5$, and $CA=4$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I n... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. An L-shape is one of the following four pieces, each consisting of three unit squares:\n\n[asy]\nsize(300);\ndefaultpen(linewidth(0.8));\npath P=(1,2)--(0,2)--origin--(1,0)--(1,2)--(2,2)--(2,1)--(0,1);\ndraw(P);\ndraw(shift((2.7,0))*ro... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. For what value of \\( p \\) is the ratio of the roots of the equation \\( x^{2} + p x - 16 = 0 \\) equal to \\( -4 \\)?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find the value ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N towns in a coordinate plane. Town i is located at coordinates (x_i, y_i). The distance b... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. From an urn containing \\( N \\) balls, of which \\( n \\) are white and \\( N-n \\) are black, a selection is made without replacement ( \\( n \\geq 2 \\) ). Consider ordered samples of size \\( M \\). What is the probability of event... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends preparing for the test. If a student receives 72 points on a test for which she spent 3 hours preparing, what s... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that the incircle of quadrilateral $ABCD$ touches sides $AB$, $BC$, $CD$, and $DA$ at points $E$, $F$, $G$, and $H$ respectively, and $AF$, $DF$, and $EG$ intersect at points $M$ and $N$. If $BF = CF = 5$ and $EG = 6$, then the l... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A box and 100 identical aluminum balls inside it weigh 510 g. The same box and 100 identical plastic balls inside it weigh 490 g. How much will the box and 20 aluminum balls and 80 plastic balls inside it weigh?"
},
{
"from": "... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In the regular triangular prism \\(ABC - A_{1} B_{1} C_{1}\\), points \\(D\\) and \\(E\\) are on the lateral edges \\(BB_{1}\\) and \\(CC_{1}\\) respectively. Given that \\(EC = BC = 2BD\\), find the size of the dihedral angle between ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A circle with center O inscribed in a convex quadrilateral ABCD is tangent to the lines\r\nAB, BC, CD, DA at points K, L, M, N respectively. Assume that the lines KL and MN\r\nare not parallel and intersect at the point S. Prove that B... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the function\n$$\nS(t)=\\left\\{\\begin{array}{l}\n2\\left(1-t+t^{2}-t^{3}\\right)\\left(0<t<\\frac{1}{2}\\right), \\\\\n\\frac{1}{2}\\left(t+\\frac{1}{t}\\right)\\left(t \\geqslant \\frac{1}{2}\\right) .\n\\end{array}\\right.\n$... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the average of all the integer values of $M$ such that $\\frac{M}{56}$ is strictly between $\\frac{3}{7}$ and $\\frac{1}{4}$?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Solve the equation\n\n\\[ y''' - 2y'' + 2y' = 4\\cos(x)\\cos(3x) + 6\\sin^2(x) \\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to solve this differential equation: y''' - 2y'' + 2y' = 4cos(x... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The proposition is: \"If \\( n \\) is a positive odd number, and the sum of its digits is 4, and none of the digits are zero, then \\( n \\) is a prime number.\"\n\nHow many counterexamples exist for the above proposition?\n(A) 0\n(B) ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a regular 16-gon \\( M \\), find the number of sets of four vertices of this 16-gon that form trapezoids."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, let's tackle this problem: finding the nu... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a circle on a plane with center \\( O \\) and a point \\( P \\) outside the circle. Construct a regular \\( n \\)-sided polygon inscribed in the circle, and denote its vertices as \\( A_{1}, A_{2}, \\ldots, A_{n} \\). Show that\n... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. If \\(A\\), \\(B\\), and \\(C\\) are the three interior angles of \\(\\triangle ABC\\), and \\(A < B < C\\) where \\(C \\neq \\frac{\\pi}{2}\\), then which of the following conclusions is correct?\nA. \\(\\sin A < \\sin C\\)\nB. \\(\\c... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.\nHe would like to rewr... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \\( S(n) \\) represents the sum of the digits of the natural number \\( n \\), for example, \\( S(123) = 1 + 2 + 3 = 6 \\). If two different positive integers \\( m \\) and \\( n \\) satisfy\n\\[\n\\left\\{\\begin{array}{l} \nm < 100 \... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find $\\begin{pmatrix} 3 & 0 \\\\ 1 & 2 \\end{pmatrix} + \\begin{pmatrix} -5 & -7 \\\\ 4 & -9 \\end{pmatrix}.$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out how to solve this ma... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a regular tetrahedron \\( P-ABC \\) with edge length 1, point \\( D \\) is the midpoint of \\( PC \\). Point \\( E \\) is a moving point on segment \\( AD \\). Determine the range of values for the angle formed between line \\( B... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Point \\( M \\) is the midpoint of side \\( AB \\) of triangle \\( ABC \\). Circle \\(\\omega_{1}\\), which is tangent to line \\( AC \\), passes through points \\( A \\) and \\( M \\). Circle \\(\\omega_{2}\\), which is tangent to lin... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nJuliana wants to assign each of the 26 letters $A, B, C, D, \\ldots, W, X, Y, Z$ of the alphabet a nonzero numerical value, such that $A \\times C = B, B \\times D = C, C \\times E = D$, and so on, up to $X \\times Z = Y$.\n\na) If J... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a right-angled triangle, the angle bisector of an acute angle divides the opposite side into segments of length 1 and 2. What is the length of the bisector?\n\nA) \\(\\sqrt{2}\\)\n\nB) \\(\\sqrt{3}\\)\n\nC) \\(\\sqrt{4}\\)\n\nD) \\(... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a Cartesian coordinate plane, a rectangle is called standard if all of its sides are parallel to the $x$- and $y$-axes, and a set of points is called nice if no two of them have the same $x$- or $y$-coordinates. Bert chooses a nice ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $S$ be a set of $2017$ points in the plane. Let $R$ be the radius of the smallest circle containing all points in $S$ on either the interior or boundary. Also, let $D$ be the longest distance between two of the points in ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Suppose that \\( x \\) and \\( y \\) are real numbers with \\( -4 \\leq x \\leq -2 \\) and \\( 2 \\leq y \\leq 4 \\). The greatest possible value of \\( \\frac{x+y}{x} \\) is:\n(A) 1\n(B) -1\n(C) \\( -\\frac{1}{2} \\)\n(D) 0\n(E) \\( \... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a tournament where each participant met every other participant exactly once, each match was judged by one referee, and all referees judged a different number of matches. Player Ivanov claims that all his matches were judged by diff... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find all monotonically increasing sequences \\(a_{1}, a_{2}, a_{3}, \\ldots\\) of natural numbers such that \\(i+j\\) and \\(a_{i}+a_{j}\\) have the same number of divisors for all \\(i, j \\in \\mathbb{N}\\)."
},
{
"from": "as... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( n \\geq 5 \\) be a natural number, and let \\( a_{1}, a_{2}, \\cdots, a_{n} \\) be \\( n \\) distinct natural numbers with the following property: for any two distinct non-empty subsets \\( A \\) and \\( B \\) of the set \\( S ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A box contains 5 black ties, 7 gold ties, and 8 pink ties. Stephen randomly chooses a tie from the box. Each tie is equally likely to be chosen. The probability that Stephen chooses a pink tie is equivalent to\n(A) \\(\\frac{1}{4}\\)\n... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. (1) Prove that \\( f(x)=\\sin |x| \\) is not a periodic function.\n\n(2) Prove that \\( y=\\sin \\sqrt[3]{x} \\) is not a periodic function."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to pr... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Heidi has now broken the first level of encryption of the Death Star plans, and is staring at the sc... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.*This is the advanced version of the [Total Primes](https://www.codewars.com/kata/total-primes/) kata.*\n\n---\n\nThe number `23` is the smal... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the smallest natural number that is divisible by 11, which after being increased by 1 is divisible by 13."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. I need to find the smallest natura... | null | null | null | null | null | null | null | null | null | null |
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