
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
A frustum of a right square pyramid is inscribed in a sphere of radius \( R \). The larger base of the frustum passes through the center of the sphere, and the lateral edge makes an angle \( \beta \) with the plane of the base. Find the volume of the frustum.

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