
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
Write the integers from 1 to 6 on the six faces of a cube so that any pair of consecutive numbers - including the pair 6 and 1 - are on adjacent faces. How many different arrangements are possible? (Two arrangements are not considered different if one can be transformed into the other by some symmetry of the cube - such as rotation or reflection on a plane through the center - or by replacing each number with the next one, with 6 replaced by 1.)

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