
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
There are two targets, A and B. A shooter shoots at target A once, with a probability of $\frac{3}{4}$ of hitting it and scoring $1$ point, or missing it and scoring $-1$ point. The shooter shoots at target B twice, with a probability of $\frac{2}{3}$ of hitting it and scoring $2$ points each time, or missing it and scoring $0$ points. The results of each shot are independent. Assuming the shooter completes all three shots, what is the probability of scoring $3$ points?

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