
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 the following four propositions:

① If $f(x+2)=f(2-x)$, then the graph of $f(x)$ is symmetric about $x=2$.

② If $f(x+2)=f(2-x)$, then the graph of $f(x)$ is symmetric about the y-axis.

③ The graphs of $y=f(2+x)$ and $y=f(2-x)$ are symmetric about $x=2$.

④ The graphs of $y=f(2+x)$ and $y=f(2-x)$ are symmetric about the y-axis. The correct proposition numbers are.

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