
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
Person A and Person B each shoot once, with the probabilities of hitting the target being $\dfrac{2}{3}$ and $\dfrac{3}{4}$, respectively. Assume that whether each shot hits the target is independent of the others. (The result must be given as a fraction.)

(1) Calculate the probability that Person A shoots 3 times and misses the target at least once;

(2) Calculate the probability that both people shoot twice, with Person A hitting the target exactly 2 times and Person B hitting the target exactly once.

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