
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
There are 20 products among which 17 are qualified and 3 are defective. Three products are randomly chosen for inspection. Determine the following:  
(1) The number of ways to choose 3 qualified products.  
(2) The probability of exactly 1 defective product in the chosen 3.  
(3) The probability that at least 2 of the chosen 3 products are not defective.

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