
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 length of the larger base of a regular quadrilateral truncated pyramid is \( a \). The lateral edge and the diagonal of the truncated pyramid form angles \(\alpha\) and \(\beta\), respectively, with the plane of the base. Find the area of the smaller base of the pyramid.

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