
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
A council consists of nine women and three men. During their meetings, they sit around a round table with the women in indistinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways can the nine chairs and three stools be arranged around the round table for a meeting?

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