
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 an oblique prism \( A B C A_{1} B_{1} C_{1} \) (where \( A A_{1} \parallel B B_{1} \parallel C C_{1} \)) is an isosceles triangle with \( A B = A C = a \) and \(\angle C A B = \alpha\). The vertex \( B_{1} \) of the upper base is equidistant from all sides of the lower base, and the edge \( B_{1} B \) forms an angle \(\beta\) with the plane of the base. Find the volume of the prism.

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