
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
There are 2002 athletes, numbered sequentially from $1, 2, 3, \cdots, 2002$. Select several athletes to form a ceremonial team, but ensure that no remaining athlete's number equals the product of the numbers of any two other remaining athletes. What is the minimum number of athletes that can be selected for the ceremonial team? Provide your selection method and briefly explain the reasoning.

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