
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 the right prism $ABC A_1 B_1 C_1 (A A_1 \parallel B B_1 \parallel C C_1)$ is an isosceles triangle $ABC$ with an angle $\alpha$ between the equal sides $AB$ and $AC$. The segment of the line joining the vertex $A_1$ of the upper base to the center of the circle circumscribed around the lower base is equal to $l$ and makes 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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