
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, products of a specific type are manufactured on three production lines. The first line produces $30\%$ of the total production, the second $25\%$, and the third the remaining part. Each line is characterized by the following respective percentages of good products: $97\%, 98\%, 96\%$. A randomly selected product from the factory turns out to be defective. Determine the probabilities that this product was manufactured on the first, second, and third lines.

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