
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 single round-robin table tennis tournament, a) 10 players, b) 11 players competed. What is the minimum number of matches the champion must have won, given that there was no tie for first place?

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