
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 proposition numbers 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) "p∨q is true" is a sufficient but not necessary condition for "p∧q is true";  
(3) If $p∧q$ is a false proposition, then both p and q are false propositions;  
(4) For proposition p: $\exists x_0 \in \mathbb{R}$, such that $x_0^2+x_0+1<0$, then $\neg p$: $\forall x \in \mathbb{R}$, $x^2+x+1\geq0$.

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