
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 workshop, on two different days, each day produced $n$ products, among which 1 defective product was produced on the first day, and 2 defective products were produced on the second day. The quality inspection department randomly selects 4 products for inspection each day. If a defective product is found, the products of that day cannot pass the inspection. It is known that the probability of passing the inspection on the first day is $\frac{3}{5}$.

(1) Find the value of $n$;  
(2) Find the probability that the products pass the inspection on both days;  
(3) Find the probability that the products pass the inspection on at least one of the two days.

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