
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 segment \(OA\). From the endpoint \(A\), 5 segments \(AB_1, AB_2, AB_3, AB_4,\) and \(AB_5\) are drawn. From each point \(B_i\), either five new segments can be drawn, or no new segments can be drawn, and so on. Can the number of free endpoints of the constructed segments be equal to 1001?

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