
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
Three couples dine every Saturday at the same restaurant, at the same round table. The restaurant's policy is:

(a) never to seat a husband and wife together as neighbors;

(b) the seating arrangement of the six at the table must be different each Saturday.

For how many Saturdays can the couples go to the restaurant without repeating the seating arrangements at the table?

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