
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
At a factory, machines \(a\), \(b\), and \(c\) produce 20%, 35%, and 45% of all products, respectively. The defect rates in their production are 3%, 2%, and 4%, respectively. What is the probability that a randomly chosen defective product was produced by machine \(a\), \(b\), and \(c\), respectively?

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