
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, B, and C are three independent machine tools processing the same type of part. It is known that the probability of part processed by machine A being first-class is unknown, and the probability that the part processed by machine B is not first-class is $\frac{1}{4}$. The probability that the part processed by machine B is first-class while the part processed by machine C is not first-class is $\frac{1}{12}$. The probability that the parts processed by machines A and C being first-class is $\frac{2}{9}$.

(I) Find the probability that the individual parts processed by machines A, B, and C are first-class.
(II) If one part is randomly selected from each machine (A, B, and C), find the probability that at least one part is first-class.

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