
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 5 products, there are 3 authentic ones and 2 defective ones. The authentic and defective products are indistinguishable by appearance. When 2 products are randomly selected from these 5, calculate the probability that:  
(1) both selected products are authentic;  
(2) one selected product is authentic and the other is defective;  
(3) at least one selected product is defective.

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