
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
Ten people arrive for dinner at a restaurant, but the circular table only seats six. If two seatings that are merely rotations of each other are considered identical, how many different ways can six of these people be chosen and seated?

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