
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 "2008 Olympic Knowledge Quiz Contest" held in a community, three participants, A, B, and C, answered a question about the Olympics simultaneously. It is known that the probability of A answering the question correctly is $\frac{3}{4}$, the probability of both A and C answering incorrectly is $\frac{1}{12}$, and the probability of both B and C answering correctly is $\frac{1}{4}$.  
(Ⅰ) Find the probability of B and C each answering the question correctly.  
(Ⅱ) Find the probability that exactly two out of A, B, and C answer the question correctly.

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