
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
A and B each take 3 shots, with A hitting the target with a probability of $\frac{1}{2}$ and B hitting the target with a probability of $\frac{2}{3}$.
(Ⅰ) Calculate the probability that A hits the target exactly 2 times;
(Ⅱ) Calculate the probability that B hits the target at least 2 times;
(Ⅲ) Calculate the probability that B hits the target exactly 2 more times than A;

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