
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 \( A_{1} \), a ray \( l_{1} \) is drawn in the direction of \( A_{2} \); from \( A_{2} \), a ray \( l_{2} \) is drawn in the direction of \( A_{3} \), and so on, from \( A_{6} \), a ray \( l_{6} \) is drawn in the direction of \( A_{1} \). From a point \( B_{1} \), taken on the ray \( l_{1} \), a perpendicular is dropped onto ray \( l_{6} \), from the base of this perpendicular another perpendicular is dropped onto \( l_{5} \), 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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