
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 line segment connecting a point on the circumference of the upper base of a cylinder to a point on the circumference of the lower base has length $l$ and makes an angle of $\alpha$ with the plane of the base. Find the distance from this line segment to the axis of the cylinder if the axial cross-section of the cylinder is a square. What are the possible values of $\alpha$?

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