
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
Given two shapes, a square and a regular pentagon, where each side of each shape is fully equal to the other. If the pentagon starts rotating counterclockwise and the square on top of it starts rotating clockwise, both sides will continue rotating until the side AE of the pentagon and side C of the square align. At this point, the square has rotated at least (_) full turns.

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