
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
Person A and Person B practice shooting, with the probabilities of hitting the target being $\frac{1}{2}$ and $\frac{1}{3}$, respectively. Both A and B shoot once, and the following statements are made:  
① The probability of the target being hit exactly once is $\frac{1}{2} + \frac{1}{3}$;  
② The probability of the target being hit exactly twice is $\frac{1}{2} \times \frac{1}{3}$;  
③ The probability of the target being hit is $\frac{1}{2} \times \frac{2}{3} + \frac{1}{2} \times \frac{1}{3} = \frac{1}{2}$;  
④ The probability of the target being hit is $1 - \frac{1}{2} \times \frac{2}{3}$;  
The correct statement(s) is/are __________.

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