
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
For a natural number  $n \ge 3$ , we draw  $n - 3$  internal diagonals in a non self-intersecting, but not necessarily convex, n-gon, cutting the  $n$ -gon into  $n - 2$  triangles. It is known that the value (in degrees) of any angle in any of these triangles is a natural number and no two of these angle values are equal. What is the largest possible value of  $n$ ?


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