
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
An ant starts from the center of one face of a cube, moves to the center of an adjacent face each time, passing through each center exactly once, and finally returns to the starting point. The total number of different sequences of centers passed through is ______. (Two sequences are considered different if the order of the centers passed through in the walking direction is different.)

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