
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
Find all natural numbers  $n\geq 3$  satisfying one can cut a convex  $n$ -gon into different triangles along some of the diagonals (None of these diagonals intersects others at any point other than vertices) and the number of diagonals are used at each vertex is even.

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