
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 triangle with a side of length \( a \) and an angle \( \alpha \) between the equal sides. The diagonal of the lateral face, opposite to this angle, forms an angle \( \varphi \) with the adjacent lateral face. Find the volume of the prism.

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