
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]


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Let $f(x)$ be an odd function defined on the real line $\mathbb{R}$, satisfying $f(x-2) = -f(x)$. When $x \in [-1, 1]$, $f(x) = x^3$. Among the four propositions below:  
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 the point $(3, 0)$.  
The correct proposition number(s) is/are _____.

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