
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 base of a pyramid is a rectangle, in which the angle between the diagonals is \(\alpha\). A sphere of radius \(R\) is circumscribed around this pyramid. Find the volume of the pyramid, if all its lateral edges form an angle \(\beta\) with the base.

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