
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
Three individuals, A, B, and C, are shooting independently. The probabilities of hitting the target for A, B, and C are $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{4}$, respectively. Let each shot be independent.<br/>$(Ⅰ)$ If B shoots twice at the same target, find the probability of hitting the target exactly once;<br/>$(Ⅱ)$ If A, B, and C each shoot once at the same target, find the probability of hitting the target.

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