
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 prism is a rhombus. One of the diagonals of the prism is equal to \(a\) and forms an angle \(\alpha\) with the base plane and an angle \(\beta\) with one of the lateral faces. Find the volume of the prism.

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