
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 acute triangle with a side length of \( a \) and an angle \( \alpha \) between the equal sides. A lateral face of the pyramid, passing through the side of the base opposite the given angle \( \alpha \), makes an angle \( \beta \) with the base plane. Find the volume of the cone circumscribed around this pyramid, assuming all its lateral edges are equal to each other.

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