
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 measuring 5 units is assembled from 125 smaller unit cubes. Two non-adjacent faces (opposite faces) of the larger cube are painted red. After painting, the large cube is disassembled into the individual unit cubes. Two of these unit cubes are selected uniformly at random. What is the probability that one of the selected unit cubes has exactly one painted face, while the other has three painted faces?

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