
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 the function $y=f(x)$ be an odd function defined on $\mathbb{R}$, and it satisfies $f(x-2)=-f(x)$ for all $x \in \mathbb{R}$. Also, when $x \in [-1,1]$, $f(x)=x^3$. Then, among the following four statements: ① The function $y=f(x)$ is a periodic function with a period of 4; ② When $x \in [1,3]$, $f(x)=(2-x)^3$; ③ The graph of the function $y=f(x)$ is symmetric about $x=1$; ④ The graph of the function $y=f(x)$ is symmetric about $(2,0)$. The correct statements are.

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