
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 with each side 5 units is composed of 125 smaller unit cubes. One entire face of the cube is painted red, and half of an adjacent face (randomly selected 12 unit cubes) is painted red. If the cube is disassembled into 125 unit cubes, and two of the unit cubes are selected uniformly at random, what is the probability that one of the selected unit cubes will have exactly one painted face while the other unit cube has no painted faces?

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