
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
Given the following propositions:  
(①) Given two non-zero vectors $\overline{m}$ and $\overrightarrow{n}$, "vector $\overrightarrow{m}$ is collinear with vector $\overrightarrow{n}$" is a necessary but not sufficient condition for "$\overrightarrow{m} \cdot \overrightarrow{n} = |\overrightarrow{m} \cdot \overrightarrow{n}|$";  
(②) Given the function $f(x)=5|x| - \frac{1}{\sqrt{2|x|-4}}$, if $a < -2$ and $b > 2$, then "$f(a) > f(b)$" is a necessary and sufficient condition for "$a+b < 0$";  
(③) The negation of the proposition "$\exists x_0 \in \mathbb{R}, x_0^2 + x_0 - 1 < 0$" is "$\forall x \in \mathbb{R}, x^2 + x - 1 \geqslant 0$";  
(④) "$a+b \neq 4$" is a sufficient but not necessary condition for "$a \neq 1$ or $b \neq 3$";  
(⑤) "$\varphi = k\pi + \frac{\pi}{2} (k \in \mathbb{Z})$" is a necessary and sufficient condition for "the function $f(x) = \sin(\omega x + \varphi) (\omega \neq 0)$ to be an even function",  
where the correct proposition numbers are ______.

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