
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 larger cube with 5 units on each side is composed of 125 smaller unit cubes. One face of the larger cube is painted red, and additionally, all unit cubes along one internal diagonal from the bottom front left to top back right of the cube are painted green (a cube at intersection is doubly painted). The cube is then disassembled into 125 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of the two selected unit cubes has exactly three painted faces while the other unit cube has exactly one painted face?

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