
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 the "Principal's Cup" comprehensive knowledge competition held at Futian Foreign Language School, the first round requires teams A, B, and C to simultaneously answer a professional knowledge question. The process of answering questions among the three teams does not affect each other. It is known that the probability of team A answering this question correctly is $\frac{3}{4}$, the probability of both teams A and C answering incorrectly is $\frac{1}{12}$, and the probability of both teams B and C answering correctly is $\frac{1}{4}$.

(1) Find the probability of teams B and C answering this question correctly, respectively;

(2) Find the probability that exactly two of the three teams A, B, and C answer this question correctly.

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