
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 teams in the area, with 4, 6, 7, and 9 students respectively. Each team has three co-captains. If I randomly select a team, and then randomly select three members of that team to give a copy of $\emph{Advanced Algebra}$, what is the probability that all three of the people who receive books are co-captains?

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