
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
(This question is worth a total of 12 points)

Person A and person B each shoot once, with the probabilities of hitting the target being $p$ and $q$, respectively. Assume that whether A or B hits the target does not affect each other; whether each person hits the target in each shot also does not affect each other.

(1) Calculate the probability that person A shoots 4 times and misses the target at least once;

(2) Calculate the probability that both persons shoot 4 times, with person A hitting the target exactly 2 times and person B hitting the target exactly 3 times.

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