
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 a line segment \(OA\). From the endpoint \(A\), 5 line segments \(AB_{1}, AB_{2}, AB_{3}, AB_{4}, AB_{5}\) emanate. From each point \(B_{i}\), either five new line segments may start, or none at all, and so on.

Can the number of free endpoints of the constructed line segments equal \(1001\)?

A free endpoint of a line segment is defined as a point that belongs to only one line segment (excluding point \(O\)).

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