
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 with 12 participants, each player played exactly one game against each of the others. A win is worth 1 point, a draw is worth \( \frac{1}{2} \) point, and a loss is worth 0 points. Vasya lost only one game but finished last with the fewest points. Petya finished first with the most points. How many points less did Vasya score than Petya?

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