
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 an odd function $f(x)$ defined on $\mathbb{R}$ that satisfies $f(x-4) = -f(x)$, and for $x \in [0, 2]$, $f(x) = \log_{2}(x+1)$. Consider the following four statements:  
① $f(3) = 1$;  
② The function $f(x)$ is increasing on $[-6, -2]$;  
③ The function $f(x)$ is symmetric about the line $x = 4$;  
④ If $m \in (0, 1)$, then the sum of all roots of the equation $f(x) - m = 0$ in $[-8, 8]$ is $-8$.  
Among these statements, the correct ones are.

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