
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
All the edges of the regular tetrahedron \(P-ABC\) have length \(1\). Let \( L, M, N \) be the midpoints of the edges \( PA, PB, PC \) respectively. Find the area of the cross-section of the circumsphere of the tetrahedron when cut by the plane \( LMN \).

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