
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
The base perimeter of an Egyptian pyramid (a regular quadrilateral pyramid) is equal to the circumference of the circle whose radius is the height of the pyramid. What is the angle between the three medians of one of the side faces and the base plane?

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