
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
Machine tools A, B, and C each independently process the same type of part. It is known that the probability of machine tool A producing a first-class part and machine tool B not producing a first-class part is $\frac{1}{4}$, the probability of machine tool B producing a first-class part and machine tool C not producing a first-class part is $\frac{1}{12}$, and the probability of both machine tools A and C producing a first-class part is $\frac{2}{9}$.  
(Ⅰ) Find the individual probabilities that machine tools A, B, and C each produce a first-class part;  
(Ⅱ) Take one part from each of A, B, and C for inspection, and find the probability of getting at least one first-class part.

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