
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 right parallelepiped is a parallelogram with diagonals \(a\) and \(b\) (\(a > b\)) and an acute angle \(\alpha\) between them. The smaller diagonal of the parallelepiped forms an acute angle \(\beta\) with the larger diagonal of the base. Find the volume of the parallelepiped.

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