
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 a function $y=f(x)$ with the domain of $\mathbb{R}$, for any $x \in \mathbb{R}$, it satisfies the conditions $f(x) + f(4-x) = 0$ and $f(x+2) - f(x-2) = 0$. For the function $y=f(x)$,  
among the following conclusions, the ones that must be correct are: (Fill in the serial numbers of all correct conclusions)  
① $y=f(x)$ is an odd function;                ② $y=f(x)$ is an even function;  
③ $y=f(x)$ is a periodic function;              ④ The graph of $y=f(x)$ is symmetric about the axis.

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