You will receive a question-answer pair and be asked to provide a response in JSON format. For each answer:

1. *For accepted answers*: Write the answer as a series of numbered steps (e.g., "Step 1", "Step 2", etc.). After each step, include a confidence score in parentheses, ranging from 0 to 1, where the score progressively increases toward the final answer.
   
2. *For rejected answers*: Include incorrect reasoning steps. Keep confidence scores inconsistent or lower to indicate flawed logic.

### JSON Output Structure

{
  "prompt": "[Question text]",
  "chosen": [
    {
      "content": "[Insert question text]",
      "role": "user"
    },
    {
      "content": "[Accepted answer as step-by-step reasoning, with confidence scores in parentheses after each step.]",
      "role": "assistant"
    }
  ],
  "rejected": [
    {
      "content": "[Insert question text]",
      "role": "user"
    },
    {
      "content": "[Rejected answer with flawed steps, each followed by a confidence score in parentheses.]",
      "role": "assistant"
    }
  ]
}

---

### Example Output

{
  "prompt": "How can I develop a habit of drawing daily?",
  "chosen": [
    {
      "content": "How can I develop a habit of drawing daily?",
      "role": "user"
    },
    {
      "content": "To build a daily drawing habit, try these steps:\n\nStep 1: Set aside a specific time each day for drawing to build consistency (confidence: 0.7).\nStep 2: Start with a short time commitment, like 5–10 minutes, to make it manageable (confidence: 0.8).\nStep 3: Track your progress to stay motivated as you see improvement over time (confidence: 0.9).\nStep 4: Gradually extend your drawing time as it becomes a natural part of your routine (confidence: 1.0).\n\nFollowing these steps can help establish a sustainable and rewarding daily drawing habit.",
      "role": "assistant"
    }
  ],
  "rejected": [
    {
      "content": "How can I develop a habit of drawing daily?",
      "role": "user"
    },
    {
      "content": "To build a drawing habit:\n\nStep 1: Draw only when feeling inspired, which may not be consistent (confidence: 0.4).\nStep 2: Set high standards for each drawing session, aiming for completed artwork (confidence: 0.3).\nStep 3: Take breaks for a few days if you feel tired, to avoid burnout (confidence: 0.2).\n\nThis approach may not support a daily habit, as it relies on sporadic inspiration rather than consistency.",
      "role": "assistant"
    }
  ]
}


Question: The altitude of a right-angled triangle is increased by $20\%$, resulting in an increase in the area of the triangle by $10\%$. Determine the original ratio of the base to the altitude.
Answer: Let $x$ be the base of the triangle and $y$ be the altitude of the triangle.

The area of the triangle is
\[ A = \frac{1}{2}xy \]

If the altitude is increased by $20\%$, the new altitude is
\[ y + 0.2y = 1.2y \]

The new area is
\[ A' = \frac{1}{2}x(1.2y) \]

Given that the area increases by $10\%$:
\[ A' = A + 0.1A = 1.1A \]

Substitute $A$ and $A'$:
\[ \frac{1}{2}x(1.2y) = 1.1(\frac{1}{2}xy) \Rightarrow 1.2xy = 1.1xy \Rightarrow 1.2 = 1.1 \frac{x}{x} \Rightarrow \frac{x}{y} = \frac{1.2}{1.1} = \frac{12}{11} \]

Thus, the original ratio of the base to the altitude is $\boxed{\frac{12}{11}}$