
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
Point $A$ is on the circumference of the upper base of a cylinder, and point $B$ is on the circumference of the lower base. The line segment $AB$ makes an angle $\alpha$ with the plane of the base and an angle $\beta$ with the plane of the axial section passing through point $B$. Find the volume of the cylinder if the length of segment $AB$ is $l$.

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