
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 statements is incorrect?

① The contrapositive of the proposition "If $x^2-3x+2=0$, then $x=1$" is "If $x \neq 1$, then $x^2-3x+2 \neq 0$".  
② "$x=1$" is a sufficient but not necessary condition for "$x^2-3x+2=0$".  
③ A necessary and sufficient condition for line $l$ to be perpendicular to plane $\alpha$ is that $l$ is perpendicular to two lines within plane $\alpha$.  
④ For the proposition $p$: $\exists x \in \mathbb{R}$ such that $x^2+x+1<0$, the negation $\neg p$ is: $\forall x \in \mathbb{R}$, $x^2+x+1 \geq 0$.

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