
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
Two identical cubes are to be painted, and each face can independently be painted red, black, or white. Calculate the probability that after they are painted, and allowed any rotation or flip, the cubes can be rotated or flipped to look identical, with at least one face of each color visible.

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