
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
A certain product is manufactured by two factories. The production volume of the second factory is three times that of the first. The defect rate of the first factory is $2\%$, whereas the defect rate of the second factory is $1\%$. Products made by both factories over the same period are mixed together and sent for sale. What is the probability that a purchased product is from the second factory, given that it is defective?

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