# Step 3: Solve, Verify, and Format Results

Solve the mathematical assignment, verify your computed results against the provided **Wolfram Alpha output**, and return the final answers in LaTeX.

## Input

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

- **Wolfram Alpha Output:**  
``` json
{{ calculationsText }}
```

## Rules

1. **Solve** the assignment using correct mathematical reasoning.  
2. **Use Wolfram Alpha Output:**  
  - Focus on section with attribute `"primary": true` or titles like `"Result"` or `"Solution"`.  
  - Treat their outputs as verified answers for comparison.  
3. **Verify** correctness by mathematical equivalence, not string matching  
   (e.g., `$0.5$` ≡ `$1/2$`).  
4. **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.
5. **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.
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.