
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
Among the four statements below, identify the correct ones (list all correct statement numbers):

1. The graph of the function $y=f(x)$ and $y=f^{-1}(x)$ are symmetric about the line $y=x$; 
2. The graph of the function $y=f(x)$ and $x=f(y)$ are symmetric about the line $y=x$;
3. The graph of the function $y=f(x)$ and $x=f^{-1}(y)$ are symmetric about the line $y=x$;
4. The graph of the function $y=f(x)$ and $x=f^{-1}(y)$ is the same curve.

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