
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
Among the following propositions:  
① The contrapositive of "If $a^2+b^2=0$, then $a$ and $b$ are both $0$" is "If $a$ and $b$ are not both $0$, then $a^2+b^2\neq0$".  
② "x=1" is a sufficient but not necessary condition for "$x^2-3x+2=0$".  
③ If $P \land q$ is a false proposition, then $P$ and $q$ are both false propositions.  
④ For the proposition $P$: There exists an $x \in \mathbb{R}$ such that $x^2+x+1<0$. The negation $\neg P$ is: There does not exist an $x \in \mathbb{R}$ such that $x^2+x+1 \geq 0$.  
The incorrect statements are.

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