
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
Cara is sitting at a circular table with six friends. Assume there are three males and three females among her friends. How many different possible pairs of people could Cara sit between if each pair must include at least one female friend?

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