
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
A group of 10 students is participating in a mathematics competition formed by teams of 4 students each. It is known that any two teams have exactly one student in common.

a) What is the maximum number of teams that a student can participate in? Provide an example of a distribution of 10 students where this maximum number can be verified.

b) Can the competition have 8 teams?

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