
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 pyramid is an isosceles triangle with a side length of \(a\) and a vertex angle of \(\alpha\). All the lateral edges are inclined to the plane of the base at an angle \(\beta\). Find the volume of the pyramid.

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