
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 tournament, each player played exactly one game against each of the other players. The winner of each game received 1 point, the loser received 0 points, and each player received $\frac{1}{2}$ point in the case of a tie. At the end of the tournament, it was observed that exactly two-thirds of the points earned by each player came from games against the eight players with the lowest scores. Determine the total number of players in the tournament.

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