
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 four propositions as follows:  
(1) The negation of the proposition "$\exists x_{0} \in \mathbb{R}, x_{0}^{2} + 1 > 3x_{0}$" is "$\forall x \in \mathbb{R}, x^{2} + 1 < 3x$";  
(2) In regression analysis, a model with a correlation index $R^{2} = 0.96$ has a better fit than a model with $R^{2} = 0.84$;  
(3) Given $a, b \in \mathbb{R}$, $p: a < b, q: \frac{1}{b} < \frac{1}{a} < 0$, then $p$ is a sufficient but not necessary condition for $q$;  
(4) Given a power function $f(x) = (m^{2} - 3m + 3)x^{m}$ is an even function, then $f(-2) = 4$.  
Among these, the correct proposition numbers are ______. (Write down all the correct proposition numbers)

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