
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 which values of \( n \) can every convex \( n \)-gon be divided into white and black triangles such that no side of a white triangle lies on the perimeter of the polygon and no sides of triangles of the same color share a segment?

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