
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
Which of the following conclusions are correct?

① The negation of the proposition "For all $x$, $x^2+x+1>0$" is: "There exists an $x$ such that $x^2+x+1<0$";  
② The converse of the proposition "If $ab=0$, then $a=0$ or $b=0$" is: "If $ab\neq 0$, then $a\neq 0$ and $b\neq 0$";  
③ If the graph of the function $f(x-1)$ is symmetric about the line $x=1$, then $f(x)$ is an even function;  
④ The graphs of the functions $y=f(x+1)$ and $y=f(1-x)$ are symmetric about the line $x=1$.

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