
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
Two identical polygons were cut out of cardboard, overlaid, and pinned together at a certain point. When one polygon is rotated around this "axis" by $25^{\circ} 30^{\prime}$, it coincides again with the second polygon. What is the minimum possible number of sides of such polygons?

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