
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
We paint the faces of a cube with 6 different colors. Each face is labeled with a number from 1 to 6, in such a way that opposite faces are labeled with the pairs (1, 6), (3, 4), and (2, 5). How many different cubes can be created in this way?

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