
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
Define a function $f(x)$ on $\mathbb{R}$ satisfying $f(x+2)+f(x)=0$, and the function $f(x+1)$ is an odd function. Consider the following statements:  
① The function $f(x)$ has a period of $T=2$;  
② The graph of the function $f(x)$ is symmetric about the point $(1,0)$;  
③ The graph of the function $f(x)$ is symmetric about the line $x=2$;  
④ The maximum value of $f(x)$ is $f(2)$;  
⑤ $f(2013)=0$.  
Among these, the correct statement(s) is/are.

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