
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 are drawn through the division points, parallel to the sides. As a result, the triangle is divided into \(n^{2}\) smaller triangles. A "chain" is defined as a sequence of triangles where no triangle appears more than once and each subsequent triangle shares a 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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