
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 5 units on each side is composed of 125 unit cubes. Two adjacent faces of the larger cube that share an edge are painted red. After disassembling the cube into 125 unit cubes, if two unit cubes are selected at random, what is the probability that one of the selected unit cubes has exactly two painted faces while the other has none?

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