
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 four propositions:  
① The proposition "If $x \geq 2$ and $y \geq 3$, then $x+y \geq 5$" is false.  
② The proposition "If $x^2-4x+3=0$, then $x=3$" has its contrapositive as "If $x \neq 3$, then $x^2-4x+30 \neq 0$."  
③ "$x>1$" is a sufficient but not necessary condition for "$|x|>0$".  
④ For the inequality $|x+1|+|x-3| \geq m$ about $x$, if its solution set is $\mathbb{R}$, then $m \leq 4$.  
The correct proposition numbers are ______.

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