
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
There are 3 math clubs in the school district, with 6, 9, and 10 students respectively. Each club has three co-presidents. If I randomly select a club, and then randomly select three members of that club to give a copy of $\emph{Introduction to Counting and Probability}$, what is the probability that exactly two of the people who receive books are co-presidents?

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