
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
There is a cuboid with dimensions $3 \times 4 \times 5$, and all six faces of it are painted. Now, this cuboid is sawed into $60$ cubes of size $1 \times 1 \times 1$. A cube is randomly selected from these small cubes.  
(1) Find the probability that a small cube has no faces painted.  
(2) Find the probability that a small cube has either $2$ faces or $3$ faces painted.

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