
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 one point, the loser received zero points, and if the game was a tie, each player earned half a point. After the tournament, it was discovered that exactly half of the points earned by each player were earned against the eight players with the least number of points. Specifically, each of the eight lowest scoring players earned half of her/his points against the other seven of these eight. Determine the total number of players in the tournament.

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