
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, each player played against every other player exactly once. The winner won half of the games and drew the other half. It turned out that the total points he scored were 9 times less than the total points scored by all the other players combined. (For a win, 1 point; for a draw, 0.5 points; for a loss, 0 points.) How many players were there in the tournament?

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