
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
Consider the following propositions:  
① If proposition p: All rational numbers are real numbers, and proposition q: The logarithm of positive numbers are negative, then the proposition "p∨q" is true;  
② There exists $x \in \mathbb{R}$ such that $x^2+x+2<0$;  
③ "Lines a and b have no common points" is a sufficient but not necessary condition for "Lines a and b are skew lines";  
④ "a=-1" is a necessary and sufficient condition for "The lines $x+ay+6=0$ and $(a-2)x+3y+2a=0$ are parallel";  
Among these, the correct propositions are (Fill in the numbers of all correct propositions).

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