
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
Given that $f(x)$ is a function defined on $\mathbb{R}$ and satisfies $f(2-x) = -f(2+x)$ and $f(x+2) = -f(x)$. Consider the following statements:

① $f(0) = 0$;  
② The function $f(x)$ is a periodic function with a period of 4;  
③ The function $f(x)$ is an odd function;  
④ The graph of function $f(x)$ is symmetric about the y-axis;  
⑤ The graph of function $f(x)$ is centrally symmetric about the point (2, 0).

Determine all the correct statements from the list above.

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