
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 integers  $n$  and  $m$ ,  $n > m > 2$ , and such that a regular  $n$ -sided polygon can be inscribed in a regular  $m$ -sided polygon so that all the vertices of the  $n$ -gon lie on the sides of the  $m$ -gon.

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