
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
If the function $y=f(x+1)$ is an even function, then the correct statements among the following are  
(1) The graph of $y=f(x)$ is symmetric about the line $x=1$  
(2) The graph of $y=f(x+1)$ is symmetric about the y-axis  
(3) It must satisfy $f(1+x)=f(-1-x)$  
(4) It must satisfy $f(1+x)=f(1-x)$.

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