
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 friends are sitting around a circular table. Each person must move to a new chair such that no one sits in the same, an adjacent, or the chair directly opposite their original seat. Calculate the number of ways they can rearrange themselves.

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