
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 regular polygon with an integer number of sides has a rotation of 360°/n, where n is the number of sides, that results in the polygon aligning with its original position. If a 50° rotation of the polygon allows it to be accurately placed back in its original position, then the smallest positive integer n that satisfies the equation 360°/n = 50° is to be found.

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