
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
It is known that the probabilities of person A and person B hitting the target in each shot are $\frac{3}{4}$ and $\frac{4}{5}$, respectively. Person A and person B do not affect each other's chances of hitting the target, and each shot is independent. If they take turns shooting in the order of A, B, A, B, ..., until one person hits the target and stops shooting, then the probability that A and B have shot a total of four times when stopping shooting is ____.

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