
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 among which 4 are defective, they are tested until all the defective products are found.

(1) If the first defective product is only found during the 5th test and the last one is found during the 10th test, how many different testing methods are there?

(2) If all the defective products are found right after the 5th test, how many different testing methods are there?

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