
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. A win granted the winner 1 point, the loser 0 points, and each player 1/2 point if there was a tie. It was found that precisely half of the points each player earned came against the twelve players with the lowest number of points. What was the total number of players in the tournament?

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