
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 $10$ different products, $4$ of which are defective, they are tested one by one until all $4$ defective products are found.
(1) If the first defective product is found in the second test, and the last defective product is found in the eighth test, how many different testing methods are there?
(2) If all $4$ defective products can be found by testing at most $6$ times, how many different testing methods are there?

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