
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 of the triangle are drawn through these division points, dividing the triangle into \( n^2 \) smaller triangles. We say that a sequence of distinct triangles is a chain if two successive triangles share a common side. What is the largest possible number of triangles in a chain?

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