
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
Let \( n \) be a positive integer greater than 7. \( P \) is a convex polygon with \( n \) sides. Any \( n-3 \) non-intersecting diagonals in \( P \) divide \( P \) into \( n-2 \) triangles. In a triangulation of \( P \), a triangle whose edges are all diagonals of \( P \) is called an internal triangle. If exactly two internal triangles exist in the triangulation of \( P \), express the triangulation of \( P \) in terms of \( n \).

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