
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
In a community, an environmental protection knowledge quiz with prizes is held. In a certain round of the competition, three participants, A, B, and C, answer a question simultaneously. It is known that the probability of A answering correctly is $\frac{1}{2}$, the probability of both A and C answering incorrectly is $\frac{1}{8}$, and the probability of both B and C answering correctly is $\frac{1}{2}$. Assume that their answers do not affect each other.<br/>$(Ⅰ)$ Find the probabilities of B and C answering correctly, respectively;<br/>$(Ⅱ)$ Find the probability that at least 2 out of A, B, and C answer correctly.

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