
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 a side length of 5 units is made up of 125 smaller unit cubes. Three adjacent faces of the larger cube (forming a corner) are painted red. After disassembling the larger cube into 125 unit cubes, two unit cubes are picked at random. What is the probability that one of the 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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