
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, shoot a target multiple times. The probability of A hitting the target is $\frac{2}{3}$, and the probability of B hitting the target is $\frac{1}{2}$. Assume that each person's shooting and hitting (or missing) the target is independent of the other's performance. After both A and B have shot the target 4 times, the probability that A hits the target exactly 2 times and B hits it exactly 3 times is _____.

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