
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
There are the following four propositions:  
① The solution to the equation $(x-1)^2+(y+1)^2=0$ is $x=1$ or $y=-1$;  
② 1 is an even number or 1 is an odd number;  
③ The negation of the proposition "The three sides of an equilateral triangle are equal";  
④ The solution set for the inequality $x^2+x+1>0$ or the inequality $x^2-x>0$ is $\mathbb{R}$.  
Among these, the false propositions are __.

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