
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
The volleyball championship at an American university is organized as follows: First, the teams play a round-robin tournament in groups of five or six. Then, the playoffs follow, to which the teams that have suffered at most one defeat in the group matches proceed. How many teams can advance from each group?

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