
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
Consider a cube that measures 5 units on each side, composed of 125 smaller unit cubes. Two faces of the larger cube that share a vertex are painted red. After disassembling the cube into 125 smaller unit cubes, two of these unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly three red-painted faces while the other unit cube has no painted faces?

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