
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
Person A and person B each conduct 3 shooting trials. The probability of person A hitting the target each time is $\frac{1}{2}$, and the probability of person B hitting the target each time is $\frac{2}{3}$. Calculate:
  1. The probability of person B hitting the target at least 2 times;
  2. The probability of person B hitting the target exactly 2 more times than person A.

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