
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]


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A warehouse receives products from three factories, where the products from the first factory comprise 20%, the second factory 46%, and the third factory 34%. It is known that the average percentage of defective items from the first factory is 3%, from the second factory 2%, and from the third factory 1%. Find the probability that a randomly selected defective item was produced at the first factory.

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