
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 coefficient $R^2 = 0.96$ has a better fit than a model with $R^2 = 0.84$;

(3) For $a, b \in \mathbb{R}$, if $p: a < b$ and $q: \frac{1}{b} < \frac{1}{a} < 0$, 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 $f(-2) = 4$.

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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