# Step 3: Solve, Verify, and Format Results

Solve the mathematical assignment, think step by step to ensure correctness, and return the final answers in LaTeX.

## Input

- **Topic:** {{ sectionName }}
- **Assignment:**  
{{ task.content }}

## Rules

1. **Independent Solution & Chain-of-Thought:**  
   - Carefully read and analyze the problem.  
   - Think step by step internally to reason through the solution.  
   - Only include reasoning **internally**, but do not output intermediate steps in the results array.
3. **Normalization:**  
  - Express results in conventional mathematical form. Prefer exact forms (`$\\frac{1}{2}$` over `$0.5$`) unless decimals are more natural.  
  - Avoid redundant or equivalent results.
4. **Atomic results:**  
  - Each element in `results` must be a complete, final answer (e.g., simplified expression, numeric value, or solved variable).  
  - Exclude reasoning steps, derivations, or partial results.  
  - Include multiple entries only if multiple distinct valid solutions exist.
5. **Normalization:**  
   - Present answers in the **most conventional form** for the assignment type.  
   - Use exact forms (`\frac{1}{2}` instead of `0.5`) unless decimals are more natural.  
   - Simplify expressions and avoid equivalent duplicates.  
6. **Formatting:**  
  - Use LaTeX for all math.  
  - Wrap formulas in `$...$`.  
  - Avoid advanced LaTeX environments (`align`, `cases`, `matrix`). Used them only if necessary.  
7. **Output:**  
  - Output JSON object as described lower in `Output` section.
  - Fill the `results` array with correctly solved and properly formatted results.

## Output JSON
Return a single valid JSON object with the following structure:
- `results` (array of strings): a list of result messages or outputs.
