
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 the pyramid is a rectangle, in which the angle between the diagonals is $\alpha$. One of the lateral edges is perpendicular to the plane of the base, and the longest edge makes an angle $\beta$ with the plane of the base. The radius of the sphere circumscribed around the pyramid is $R$. Find the volume of the pyramid.

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