
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
72 vertices of a regular 3600-gon are painted red in such a way that the painted vertices form the vertices of a regular 72-gon. In how many ways can 40 vertices of this 3600-gon be chosen so that they form the vertices of a regular 40-gon and none of them are red?

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