
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 an isosceles trapezoid with bases equal to \(a\) and \(b\) (\(a > b\)), and the acute angle is \(\alpha\). A plane passing through the larger base of the top trapezoid and the smaller base of the bottom trapezoid makes an angle \(\beta\) with the plane of the bottom base. Find the volume of the prism.

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