
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 "$|x|>1$";  
(3) If both p and q are false propositions, then p and q are both false propositions;  
(4) For the proposition p: "There exists $x \in \mathbb{R}$, such that $x^2+x+1<0$", the negation $\neg p$ is: "For all $x \in \mathbb{R}$, $x^2+x+1 \geq 0$"

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