
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 club decides to create five different committees. Each member of the club is required to join exactly three different committees. It is mandated that each trio of committees should have exactly one member in common. How many members must the club have to satisfy these conditions?
A) 12
B) 10
C) 8
D) 15

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