
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
Let $f(x)$ be an odd function defined on $(-\infty,+\infty)$, and it satisfies $f(x+2)=-f(x)$. Among the following statements about $f(x)$, the correct ones are:

① $f(4)=0$;  
② $f(x)$ is a function with a period of 4;  
③ The graph of $f(x)$ is symmetric about $x=1$;  
④ The graph of $f(x)$ is symmetric about $x=2$.

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