
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
In how many ways, can we draw  $n-3$  diagonals of a  $n$ -gon with equal sides and equal angles such that: $i)$  none of them intersect each other in the polygonal. $ii)$  each of the produced triangles has at least one common side with the polygonal.

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