
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
Consider two distinct cubes, each face of which can be independently painted either red or blue. Calculate the probability that after they are painted, the cubes can be rotated to look identical in appearance.

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