# Task

The task is to generate a **Socratic-style hint** that guides the student toward the next milestone step in solving a mathematical assignment. The hint should not reveal calculations, intermediate results, or the final answer. It should be concise, question-oriented, and encourage critical thinking.  
Hints are provided in **batches**, so assume that the student has already seen all previous hints in this sequence. Each new hint should therefore build upon earlier ones and avoid repetition.

# Previous hints

{{#hints}}
  - {{ . }}
{{/hints}}
{{^hints}}
  No previous hints.
{{/hints}}

# Assignement Content

{{ task.content }}

**Results**
{{#task.results}}
  - {{ . }}
{{/task.results}}
{{^task.results}}
  No results.
{{/task.results}}

# Output JSON Schema

- content (string): formulated hint content

# Step-by-step Instructions

- Read the **Assignment** and the **Correct result**.
- Be aware that this hint is part of a **sequence of hints**. Do not repeat earlier hints; instead, build on them.
- Identify the immediate conceptual or procedural **next milestone** (the next sub-goal that advances toward the solution).
- Compose a **Socratic hint** that:
  - Is phrased as a question or a short prompt that encourages student thinking.
  - Points to a key observation, choice of method, or relationship the student should consider.
  - **Does NOT** contain computations, intermediate numeric results, or the final answer.
  - Is no longer than **2 sentences**.
- Optionally include **one micro-step** indicating which concept, identity, or formula to consider — but **do not** perform or show the calculation.
- If multiple routes are possible, prefer the route that reveals the least information yet most likely leads to the correct result.
- Verify mentally that following the hint would lead toward the **Correct result** but **do not** reveal it.
{{^format.isEnglish}}
- **Translation**
  - Translate the formatted content and its results into the target language: {{ format.languageName }} ({{ format.languageCode }}).
  - Use correct mathematical and domain-specific terminology.
  - DO NOT TRANSLATE any LaTeX formatting.
{{/format.isEnglish}}
- **LaTeX Formatting**
  - Inline math expressions must be wrapped with `$...$`.
  - Proper LaTeX formatting should be used for all mathematical symbols, operators, and functions.
  - Avoid advanced LaTeX environments (e.g., `align`, `cases`, `matrix`, `text`, `displaystyle`), since they may not render in all contexts.
- **Produce the output**
  - Return a JSON object as described in section `Output JSON schema`.