
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 identical cubes are to be painted where each face of a cube can be independently painted Red, White, or Blue. Find the probability that after they are painted, all three cubes can be rotated to look identical.

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