
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 Let $x, y \in \mathbb{R}$, then "if $x \geq 2$ and $y \geq 2$", it is a necessary but not sufficient condition for "$x^2 + y^2 \geq 4$";  
② The negation of the proposition "All integers divisible by 2 are even" is: "There exists an integer divisible by 2 that is not even";  
③ Given the proposition "If $|a| \leq 1$, then the solution set of the inequality $(a^2 - 4)x^2 + (a + 2)x - 1 \geq 0$ with respect to $x$ is empty", its converse proposition is a false proposition;  
④ "m = 1" is a necessary and sufficient condition for "The line $(m + 2)x + my + 1 = 0$ and the line $(m - 2)x + (m + 2)y - 3 = 0$ to be perpendicular to each other";  
Then, the correct proposition numbers are    ．

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