
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
Eight people arrive for dinner, but the round table only seats seven. If two seatings that are rotations of each other are seen as identical, how many different ways can we choose seven people and seat them at the table?

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