
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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Before a company launches a product, it must conduct product inspections. When the company sends a batch of products to a merchant, the merchant is also required to randomly inspect a certain number of products according to the contract, in order to decide whether to accept the batch of products.  
(I) If the probability of each product in the company's warehouse being qualified is 0.8, and 4 products are randomly taken for inspection, calculate the probability that at least one product is qualified.  
(II) If the company sends 20 products to the merchant, including 3 that are unqualified, the merchant will randomly take 2 products for inspection according to the contract. The batch of products is accepted only if both are qualified; otherwise, it is rejected. Calculate the probability that the merchant draws 1 and 2 unqualified products, respectively, and calculate the probability that the merchant rejects the batch of products.

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