
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
Given two cubes are to be painted, with each face being painted independently and at random to be either black, white, or red, find the probability that after they are painted, at least four faces on each cube are black, and the cubes can be rotated to be identical in appearance.

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