
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 plays exactly one game with every other player. The winner of a game receives 1 point, the loser receives 0 points, and in case of a draw, each player receives $\frac{1}{2}$ point. At the end of the tournament, it is found that each player's total score consists exactly half of the points they earned from games against the 10 lowest-scoring players (and half of the points for the 10 lowest-scoring players came from games among themselves). Determine the total number of players participating in the tournament.

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