
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
A plane passing through a generator of a cylinder forms an acute angle \(\alpha\) with the plane of the axial section containing the same generator. The diagonal of the rectangle obtained in the section of the cylinder by this plane is equal to \(l\) and forms an angle \(\beta\) with the base plane. Find the volume of the cylinder.

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