
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 probabilities of the parts processed by machine tools A, B, and C being first-class are 0.7, 0.6, and 0.8, respectively. The number of parts processed by machine tools B and C are equal, and the number of parts processed by machine tool A is twice that of machine tool B.

(1) One part is taken from each of the parts processed by A, B, and C for inspection. Calculate the probability that there is at least one first-class part.

(2) The parts processed by the three machine tools are mixed together, and one part is randomly selected for inspection. Calculate the probability that it is a first-class part.

(3) The parts processed by the three machine tools are mixed together, and four parts are randomly selected for inspection. Calculate the probability that the number of first-class parts is not less than 3.

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