
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 participant played exactly once against all others. The winner of each game received $1$ point, the loser $0$ points, and each scored $\frac{1}{2}$ point if the game was a draw. At the end of the tournament, it was found that exactly half of the points each player obtained came from playing against the twelve players with the lowest scores. Notably, each of these twelve lowest scoring participants got half of their points from games among themselves. Determine the total number of participants in the tournament.

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