
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. Three faces of the larger cube that share a vertex are painted blue, and the cube is disassembled into 125 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly three painted faces while the other unit cube has no painted faces?

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