
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
A cube, each face of which is painted, is cut into 27 smaller cubes of equal size. What is the probability that any two of these smaller cubes selected at random will both have exactly two faces painted?

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