
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 are evenly spaced around a circular table, each occupying one chair. They all get up and then must sit down again such that no one sits in their original chair, the chairs directly adjacent to it, or two positions away from it. Each chair must again be occupied by one person. Find the number of valid seating arrangements.

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