
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
Consider a club that needs to assign its members to several committees. The club rules are as follows:
1. Every member must be part of exactly two different committees.
2. Each pair of committees has exactly one member in common.
Given that there are 5 committees in total within the club, determine the number of members needed to fulfill these conditions.
A) 9
B) 10
C) 11
D) 12

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