
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 person A hitting the target is $\frac{3}{4}$ and the probability of person B hitting the target is $\frac{4}{5}$, and they take turns shooting in the order of A, B, A, B, ..., calculate the probability that A has shot twice when they stop shooting.

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