
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 exactly one game against each of the other players. In each game, the winner was awarded 1 point, the loser got 0 points, and each of the two players earned 0.5 points in the case of a tie. After the tournament ended, it was discovered that exactly half of the points earned by each player came from games against the eight players with the least number of total points. (Specifically, each of these eight lowest-scoring players earned half of his/her points against the other seven of the eight). How many players were there in total in the tournament?

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