
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
Twelve women sit in 12 seats in a line. All of the 12 get up and then reseat themselves using all 12 seats, each sitting in the seat she was in before, a seat next to the one she occupied before, or skipping exactly one seat to either side (if available). Determine the number of ways the women can be reseated.

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