
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 an even function $f(x)$ on $\mathbb{R}$ that satisfies $f(x+1) = -f(x)$ and $f(x)$ is increasing on the interval $[-1, 0]$. Consider the following four statements:  
① $f(x)$ is a periodic function;  
② The graph of $f(x)$ is symmetric about $x=l$;  
③ $f(x)$ is a decreasing function on the interval $[l, 2l]$;  
④ $f(2) = f(0)$,  
Among these statements, the correct ones are. (Please list all the correct statement numbers)

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