
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
In a right square pyramid, a section parallel to the base is made. A line passing through a vertex of the base and the opposite vertex (i.e., not belonging to the same face) of the section forms an angle $\alpha$ with the plane of the base. Find the area of the section if the slant edge of the pyramid is equal to the diagonal of the base and equals $a$.

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