
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 polygon is said to be friendly if it is regular and it also has angles that, when measured in degrees, are either integers or half-integers (i.e., have a decimal part of exactly 0.5). How many different friendly polygons are there?

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