
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 \( A B C A_{1} B_{1} C_{1}\left(A A_{1}\left\|B B_{1}\right\| C C_{1}\right) \) is an isosceles triangle \( A B C \) \((AB = AC)\), with a perimeter of \( 2p \) and an angle at vertex \( A \) equal to \( \alpha \). A plane passing through the side \( BC \) and vertex \( A_{1} \) forms an angle of \( \beta \) with the base plane. Find the volume of the prism.

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