
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
Suppose there are $3$ defective products in $100$ items. If $5$ items are randomly selected, calculate the number of ways for each of the following scenarios:
$(I)$ No defective product;
$(II)$ Exactly two defective products;
$(III)$ At least two defective products.

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