
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 chess tournament with 300 participants, where each pair of participants can play at most one match, and there is no group of three participants who have all played against each other, find the maximum value of $n$ such that each participant can play at most $n$ matches.

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