
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 rectangular prism that measures 4 units by 3 units by 3 units, composed of 36 unit cubes. One face measuring 4 units by 3 units and another face measuring 3 units by 3 units that share a side are painted red. The prism is then disassembled into 36 smaller cubes. If two of the unit cubes are selected uniformly at random, calculate the probability that one of two selected unit cubes will have exactly one painted face while the other unit cube has no painted faces.

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