
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
Among 12 products, there are 10 genuine ones and 2 defective ones. If 3 products are randomly selected from these 12 products, find:<br/>$(1)$ How many different ways can the 3 products be selected?<br/>$(2)$ How many ways are there to select exactly 1 defective product among the 3 selected products?<br/>$(3)$ How many ways are there to select at least 1 defective product among the 3 selected products?

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