
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 one shot, with the probabilities of hitting the target being $\frac{2}{3}$ and $\frac{3}{4}$, respectively. Assuming the shots by A and B are independent of each other, and their respective shots are also independent, calculate the probability that A hits the target exactly twice and B hits the target exactly three times after they each shoot four times.

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