
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 different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black, white, or red. Moreover, no two adjacent faces can have the same color. Calculate the probability that after they are painted, the cubes can be rotated to be identical in appearance.

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