
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
A certain frog that was placed on a vertex of a convex polygon chose to jump to another vertex, either clockwise skipping one vertex, either counterclockwise skipping two vertexes, and repeated the procedure.
If the number of jumps that the frog made is equal to the number of sides of the polygon, the frog has passed through all its vertexes and ended up on the initial vertex, what´s the set formed by all the possible values that this number can take?


*Andrei Eckstein*

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