
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
Two individuals, A and B, each conduct 3 shooting trials. The probability of A hitting the target in each trial is $\frac{1}{2}$, while the probability of B hitting the target in each trial is $\frac{2}{3}$. The problem asks for the following:

1. The probability that A hits the target exactly 2 times.
2. The probability that B hits the target at least 2 times.
3. The probability that B hits the target exactly 2 more times than A.

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