
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 cubes are each painted on all faces, where each face is independently painted either green or red. Determine the probability that after they are painted, the two cubes can be rotated to look identical.
**A** $\frac{9}{64}$  
**B** $\frac{289}{2048}$  
**C** $\frac{45}{2048}$  
**D** $\frac{147}{1024}$  
**E** $\frac{589}{4096}$

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