
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
Four math teams in a region consist of 6, 8, 9, and 11 students respectively. Each team has three co-captains. If you randomly select a team, and then randomly select two members from that team to gift a copy of *Introduction to Geometry*, what is the probability that both recipients are co-captains?

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