
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
People are standing equally spaced around a circle, and each person knows exactly $3$ of the other $11$ people, the $2$ people standing next to him or her, as well as one additional person who is three positions away clockwise. Calculate the number of ways the $12$ people can split into $6$ pairs so that the members of each pair know each other.

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