
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
For the function $y=f(x)$ with domain $D$, the correct statement(s) is(are) (only the number of the statement is required):
① If $f(-1)=f(1)$ and $f(-2)=f(2)$, then $y=f(x)$ is an even function on $D$;  
② If $f(-1)<f(0)<f(1)<f(2)$, then $y=f(x)$ is an increasing function on $D$;  
③ If $f'(2)=0$, then $y=f(x)$ must have a local maximum or minimum at $x=2$;  
④ If $\forall x \in D$, $f(x+1)=f(-x+3)$ holds, then the graph of $y=f(x)$ is symmetric about the line $x=2$.

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