
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
Points \(A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}\) divide a circle of radius 1 into six equal parts. From \(A_{1}\), ray \(l_{1}\) is drawn in the direction of \(A_{2}\); from \(A_{2}\), ray \(l_{2}\) is drawn in the direction of \(A_{3}\), and so on, until from \(A_{6}\), ray \(l_{6}\) is drawn in the direction of \(A_{1}\). From point \(B_{1}\), located on ray \(l_{1}\), a perpendicular is dropped to ray \(l_{6}\). From the base of this perpendicular, another perpendicular is drawn to \(l_{5}\), and so on. The base of the sixth perpendicular coincides with \(B_{1}\). Find the segment \(B_{1} A_{1}\).

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