
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
There are two shooters, A and B. The probability of A hitting the target in a single shot is $\frac{1}{2}$, and the probability of B hitting the target in a single shot is $\frac{1}{3}$.

(I) If each shooter takes one shot, and the target is considered hit if at least one shot hits the target, what is the probability of hitting the target?

(II) If each shooter takes two shots, and the target is considered hit if at least three shots hit the target, what is the probability of hitting the target?

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