
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
King Arthur summons 6 knights to his castle, each of whom has exactly 2 friends among the knights. They sit around a round table (see picture for names and seats) and discover that each pair of adjacent knights are exactly friends. King Arthur wants to rearrange the seating. How many different ways can King Arthur arrange the seating such that no knight is seated next to their friends? (Arrangements that are rotations of each other are considered the same).

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