
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 a larger cube, 3 units on each side, composed of 27 smaller unit cubes. Two faces of the larger cube that share an edge are painted red. After disassembling the cube into 27 unit cubes, calculate the probability that one of two randomly selected unit cubes has exactly two painted faces, while the other has no painted faces.

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