
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 of the same size are to be painted, with the color of each face chosen independently and at random from three colors: black, white, or red. A condition stipulates that red faces on the cube cannot be adjacent. What is the probability that after they are painted, the cubes can be rotated so they look identical in appearance?
A) $\frac{1}{1024}$
B) $\frac{1}{2048}$
C) $\frac{1}{4096}$
D) $\frac{1}{5776}$
E) $\frac{1}{729}$

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