
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 the function $y=f(x)$ defined on $\mathbb{R}$. The following four statements are provided for judgment:  
(1) If for all $x \in \mathbb{R}$, we have $f(4-x) = f(4+x)$, then the graph of the function $y=f(x)$ is symmetric about the line $x=4$;  
(2) If for all $x \in \mathbb{R}$, we have $f(4-x) = f(x-4)$, then the graph of the function $y=f(x)$ is symmetric about the y-axis;  
(3) The graphs of the functions $y=f(4-x)$ and $y=f(4+x)$ are symmetric about the y-axis;  
(4) The graphs of the functions $y=f(4-x)$ and $y=f(x-4)$ are symmetric about the line $x=4$.  
Among these, the correct judgments are marked by their statement numbers.

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