
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
Some students at a school were divided into teams satisfying the following conditions:

i) Any 2 different teams have exactly 2 members in common.

ii) Each team has exactly 4 members.

iii) For any 2 students, there is a team that neither of them is part of.

a) Explain why any pair of students can participate in at most 3 teams.

b) What is the maximum number of teams?

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