
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 side of the base of a regular quadrilateral pyramid is equal to \( a \), and the angle between the lateral edge and the base plane is \( \alpha \) (\( \alpha > \pi / 4 \)). Find the area of the section of the pyramid by a plane passing through the vertex of the base and perpendicular to the opposite lateral edge (i.e., the edge not lying with this vertex in one lateral face).

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