
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
Determine which of the following statements are correct:

① The negation of the proposition "For every $x$, $x^2 + x + 1 > 0$" is "There exists an $x$ such that $x^2 + x + 1 < 0$."

② The negation 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 point $(1, 0)$, then $f(x)$ is an odd 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}
user