
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
Six people are sitting at a round table. Let \(f \geq 0\) be the number of people sitting next to at least one female, and \(m \geq 0\) be the number of people sitting next to at least one male. Determine the number of possible ordered pairs \((f, m)\).

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