
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
Two people, A and B, each shoot once, with probabilities of hitting the target being $\frac{2}{3}$ and $\frac{3}{4}$, respectively. It is assumed that the shooting of the two people does not affect each other, and the hitting probability of each person does not affect each other either.  
$(1)$ Find the probability that both A and B hit the target with one shot each.  
$(2)$ Find the probability that A shoots 4 times and hits the target exactly 3 times in a row.  
$(3)$ If B will be terminated after missing the target consecutively 2 times during shooting, find the probability that B will be terminated after shooting exactly 4 times.

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