
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 tetrahedron \( P-ABCD \) is circumscribed around a sphere of radius 1. If the distances from the center of the sphere to each of the tetrahedron's faces are equal, then the area of the base of the tetrahedron is ______.

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