
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
A certain product is classified into three grades: first-grade, second-grade, and defective. Both first-grade and second-grade products are considered as quality products. There are 6 units of this product, and 2 units are randomly selected for inspection.
(1) If among the 6 units, there are 3 first-grade, 2 second-grade, and 1 defective product:
① What is the probability that both inspected units are first-grade?
② What is the probability that exactly one of the inspected units is second-grade?
(2) If the probability that at most one of the inspected units is defective is not less than $\frac{4}{5}$, what is the maximum number of defective units among the 6 units?

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