
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 gathering of \(2n\) people, if any two individuals have the same number of friends, then those two individuals do not share any common friends (friendship is mutual). What is the maximum number of pairs of friends in this gathering?

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