
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
In a company, some pairs of people are friends (if \(A\) is friends with \(B\), then \(B\) is friends with \(A\)). It turned out that for any selection of 101 people from this company, the number of pairs of friends among them is odd. Find the maximum possible number of people in such a company.

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