
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
If $f(x)$ is an odd function defined on $\mathbb{R}$, and $f(x-2) = -f(x)$, consider the following four statements:  
(1) $f(2) = 0$; (2) $f(x)$ is a function with a period of 4; (3) The graph of $f(x)$ is symmetric about the line $x=0$; (4) $f(x+2) = f(-x)$. Among these, the correct statements are.

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