
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
Given that there are $8$ different products, among which $3$ are defective, they are tested one by one until all defective products are found.
$(1)$ If the first defective product is found exactly on the second test and the last defective product is found on the sixth test, how many different testing methods are there?
$(2)$ If at most $5$ tests are needed to find all defective products, how many different testing methods are there?

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