
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. Two faces of the larger cube that share an edge are painted red, and the cube is disassembled into 125 unit cubes. One of the unit cubes is selected at random. What is the probability that the selected unit cube has exactly one painted face?

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