
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
The following propositions:  
① "x=1" is a sufficient but not necessary condition for "x^2−3x+2=0";  
② The contrapositive of the proposition "If x^2−3x+2=0, then x=1" is "If x≠1, then x^2−3x+2≠0";  
③ For the proposition p: There exists x>0 such that x^2+x+1<0, then ¬p: For all x≤0, x^2+x+1≥0;  
④ If p∨q is a false proposition, then both p and q are false propositions;  
The correct proposition numbers are (fill in all the numbers of the correct propositions).

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