
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
Given a convex $n$-gon \( A_{n} \), where no three diagonals intersect at the same point, determine:
(1) The number of diagonals in \( A_{n} \).
(2) The number of triangles (referred to as the internal triangles of \( A_{n} \)) formed by the sides and diagonals of \( A_{n} \).

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