
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 a regular tetrahedron $P-ABC$ where all edges are of length $1$, and points $L$, $M$, and $N$ are the midpoints of edges $PA$, $PB$, and $PC$ respectively. Find the area of the cross-section of the circumscribed sphere of the tetrahedron made by the plane $LMN$.

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