
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
(1) If 19 teams participate in a round-robin tournament, find the maximum number of "friendly groups."
(2) If 20 teams participate in a round-robin tournament, find the maximum number of "friendly groups."

Note: A "friendly group" is defined as a set of three teams (A, B, and C) where team A beats team B, team B beats team C, and team C beats team A.

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