
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 one match against every other participant. A winner of a match earns 1 point, while the loser gets no points. If the match is a draw, both players score $\frac{1}{2}$ point. At the culmination of the tournament, it was observed that each player garnered exactly half of their points against the twelve players who scored the least. Each of these twelve players accumulated half of their points playing against the other eleven of these twelve. How many participants were there in total in the tournament?

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