
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 school's soccer championship, each team must play one match against every other team. The winning team of each match gets 2 points, each team gets 1 point in the case of a tie, and the losing team gets 0 points. It is known that one team has the most points (each of the other teams has fewer points than this team), but this team has fewer wins than any other team. What is the minimum number of teams that must participate?

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