
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
Consider a function $y = f(x)$ defined on the domain $\mathbb{R}$ that is an odd function satisfying the condition $f(x-2) = -f(x)$ for all $x \in \mathbb{R}$. It is also given that for $-1 \leq x \leq 1$, $f(x) = x^3$. Among the following four statements:  
① $f(x)$ is a periodic function with period 4;  
② The analytic expression of $f(x)$ on $[1, 3]$ is $f(x) = (2-x)^3$;  
③ The equation of the tangent line of $f(x)$ at the point $\left( \frac{3}{2}, f\left( \frac{3}{2} \right) \right)$ is $3x + 4y - 5 = 0$;  
④ $x = \pm 1$ are the axes of symmetry for the graph of the function $f(x)$.  
The correct statements are ______________.

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