
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 that the probabilities of person A and person B hitting the target in each shot are $\frac{3}{4}$ and $\frac{4}{5}$, respectively, and that each shot is independent. If they take shots in the order of A, B, A, B, until one of them hits the target and then stop shooting, what is the probability that A has taken two shots when they stop shooting?

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