
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 certain tournament, every player played exactly one game against each of the other players. Each game's winner scored $1$ point, the loser scored $0$ points, and each of the two players scored $\frac{1}{2}$ point in case of a tie. After the tournament ended, it was found that exactly half of the points that each player scored came from games played against the twelve players with the fewest points. What was the total number of players in this tournament?

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