
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
Given the segment \(OA\). From the end of the segment \(A\), 5 segments \(AB_{1}, AB_{2}, AB_{3}, AB_{4}, AB_{5}\) emanate. From each point \(B_{i}\), five new segments can either emanate or none at all, and so on. Can the number of free ends of the constructed segments equal 1001? By a free end of a segment, we mean a point belonging to only one segment (except for point \(O\)).

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