
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
Rectangle $ABCD$ has sides $AB=4$ and $AD=3$. Triangle $ADC$ is folded along $AC$ to form triangle $AD'C$ such that plane $AD'C$ is perpendicular to plane $ABC$. Point $F$ is the midpoint of $AD'$, and point $E$ is a point on $AC$. Consider the following statements:  
1. There exists a point $E$ such that $EF\parallel$ plane $BCD'$;  
2. There exists a point $E$ such that $EF\perp$ plane $ABD'$;  
3. There exists a point $E$ such that $D'E\perp$ plane $ABC$;  
4. There exists a point $E$ such that $AC\perp$ plane $BD'E$.  
The correct statement(s) is/are __________. (Write down all correct statement numbers)

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