
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. Winners received $1$ point, losers got $0$ points, and each player obtained $\frac{1}{2}$ point in the event of a tie. After the tournament ended, it was observed that exactly half of the points earned by each player were earned against the twelve players with the lowest number of points. (Specifically, each of the twelve lowest scoring players earned half of their points against the other eleven of the twelve). Determine the total number of players in the tournament.

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