
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 twice, with the probability of hitting the target each time being $\frac{3}{4}$. Hitting the target once scores 1 point, and missing scores 0 points. The shooter then shoots at target B once, with a hitting probability of $\frac{2}{3}$, scoring 2 points if hit, and 0 points if missed. Assume that the results of each shot are independent. The shooter performs the three aforementioned shots.
(I) Find the probability that the shooter hits exactly two shots.
(II) Find the probability distribution and the mathematical expectation EX of the shooter's total score X.

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