
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Each side of an equilateral triangle is divided into \( n \) equal parts. Lines parallel to the sides are drawn through the division points. As a result, the triangle is divided into \( n^{2} \) smaller triangles. We define a chain as a sequence of these smaller triangles, where no triangle appears more than once and each consecutive triangle shares a common side with the previous one. What is the maximum possible number of triangles in such a chain?

Present the answer in LaTex format: \boxed{Your answer}
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