
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 different cubes of the same size are to be painted, with the color of each face being chosen independently at random to be either black, white, or red. What is the probability that after they are painted, the cubes can be rotated to look identical?
**A)** $\frac{457}{431441}$
**B)** $\frac{1178}{531441}$
**C)** $\frac{917}{312441}$
**D)** $\frac{359}{218791}$

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