
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 4 math clubs in the school district, with numbers of students being 6, 9, 10, and 12 respectively. At every beginning of a math session, two students are randomly selected to be co-presidents. If a club is randomly selected, and then four members of that club are chosen at random to receive a book titled $\emph{Mastering Combinatorics}$, what is the probability that both temporary co-presidents are among the four students?

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