
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, 30 players participated, each playing exactly one game with every other player. A win was awarded 1 point, a draw 0.5 points, and a loss 0 points. What is the maximum number of players that could have exactly 5 points at the end of the tournament?

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