
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
If a function $f(x)$ defined on $(0,+\infty)$ satisfies the condition that for any two distinct real numbers $x_{1}$ and $x_{2}$, $x_{1}f(x_{1})+x_{2}f(x_{2}) > x_{1}f(x_{2})+x_{2}f(x_{1})$, then the function $f(x)$ is called a "Z function". Among the following four functions defined on $(0,+\infty)$:

1. $y=-x^{3}+1$
2. $y=x+\sin x$
3. $y=e^{x}(2x-1)$
4. $y=2(x-\ln x)+\dfrac{2x-1}{{x}^{2}}$

The serial numbers corresponding to the "Z function" are $\boxed{2, 3, 4}$.

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