
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 the probability of a genuine electronic watch is $\frac{3}{4}$ and the probability of a defect is $\frac{1}{4}$, a batch of these electronic watches is being tested. Let $X$ be the number of tests until a genuine product is detected for the first time. Find the probability $P(X=3)$.

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