
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
(1) Monitoring data in a certain region shows that the probability of air quality being good in a day is 0.8, and the probability of it being good for two consecutive days is 0.6. Given that the air quality is good on a certain day, what is the probability that it will be good the following day?  
(2) There is a batch of products of the same model. It is known that 25% are produced by Factory 1, 35% by Factory 2, and 40% by Factory 3. The defective rates of the products from these three factories are 5%, 4%, and 2% respectively. What is the probability of randomly selecting a defective product from this batch?

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