
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 statements:  
① $f(3) = 1$; ② The function $f(x)$ is increasing on the interval $[-6, -2]$; ③ The graph of the function $f(x)$ is symmetric about the line $x=1$; ④ If $m \in (0, 1)$, then the sum of all roots of the equation $f(x) - m = 0$ on the interval $[-8, 16]$ is $12$.  
Among these statements, the correct ones are:

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