problem stringclasses 20 values | answer stringclasses 15 values | init_response stringclasses 20 values | success_rate float64 0 1 | progress stringlengths 5 8 | action stringclasses 2 values | prefix stringlengths 8 45.2k | tokenized_conv stringlengths 181 45.5k | responses sequencelengths 20 20 | rewrads sequencelengths 20 20 | mean_reward float64 0 1 |
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 7 / 94 | Continue | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["Alternatively, let's consider triangle ABD and triangle ACD, but perhaps that's not the right path(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 7 / 94 | Terminate | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["\n\nOkay, after considering all the given information, let's proceed step by step.\n\nGiven:\n- si(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 17 / 94 | Continue | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["Wait, but perhaps that might complicate things.\n\nAlternatively, perhaps assign coordinates such (...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 17 / 94 | Terminate | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["\n\nWe have triangle ABC with angle A having sin A = 4/5. Point D is such that AD is the angle bis(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 21 / 94 | Continue | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["Alternatively, perhaps this coordinate system is better:\n\nLet’s assign point A at (0,0), point(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 21 / 94 | Terminate | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["\n\nAlright, let's proceed step by step.\n\nGiven triangle \\( ABC \\), with \\( \\sin \\angle A =(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 35 / 94 | Continue | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["- Point B is at (c,0)\n- Point D is at (x,y)\n- Point C is at (3k,4k)\n\nTherefore, vector DB is ((...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 35 / 94 | Terminate | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["\n\nGiven the problem, after careful consideration, we can determine that AB + AC can be expressed(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 49 / 94 | Continue | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["Wait, no.\n\nWait, original cross-multiplied equation:\n\n4[ (c -9k)^2 +144k^2 ]=9[ (2c -12k)^2 +2(...TRUNCATED) | [
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"In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point(...TRUNCATED) | 34 | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | 0 | 49 / 94 | Terminate | "Okay, so I've got this geometry problem here, and I need to figure it out step by step. Let's see.\(...TRUNCATED) | "<｜begin▁of▁sentence｜><｜User｜>In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\(...TRUNCATED) | ["\n\nTo solve the problem, we start by noting that triangle ABC has angle A with sin(A) = 4/5 and a(...TRUNCATED) | [
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