
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
In a batch of 100 products, there are 98 qualified products and 2 defective ones. During product inspection, 3 products are randomly selected from the 100 products.  
(1) How many different ways are there to select the 3 products?  
(2) How many ways are there to select exactly 1 defective product out of the 3?  
(3) How many ways are there to select at least 1 defective product out of the 3?

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