
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, the correct ones are:  
① The contrapositive of the proposition "If $x^2-3x+2=0$, then $x=1$" is "If $x\neq1$, then $x^2-3x+2\neq0$".  
② If $p\land q$ is a false proposition, then both $p$ and $q$ are false propositions.  
③ For the proposition $p$: There exists $x\in\mathbb{R}$ such that $x^2+x+1<0$, the negation $\neg p$ is: For any $x\in\mathbb{R}$, $x^2+x+1\geq0$.  
④ "$x>2$" is a sufficient but not necessary condition for "$x^2-3x+2>0$".

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