
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 \( n \) players participating in a round-robin chess tournament, where each player competes exactly once against every other player. The winner of a match earns 3 points, a draw gives each player 1 point, and the loser earns 0 points. If the total sum of all players' points is 120, what is the maximum number of participants in the tournament?

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