
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
A school is holding a round-robin football tournament. Each participating team plays one match against every other team. Winning a match earns 2 points, a draw earns 1 point, and losing a match earns 0 points. It is known that only one team has the highest total points, but it has the fewest number of wins. What is the minimum number of teams participating for this scenario to be possible?

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