
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]


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Given a function $f(x)$ defined on $\mathbb{R}$, if for any two distinct real numbers $x\_1$, $x\_2$, we have $x\_1 f(x\_1) + x\_2 f(x\_2) > x\_1 f(x\_2) + x\_2 f(x\_1)$, then the function $f(x)$ is called an "H function". Find the serial number(s) of the "H function(s)" in the following list:
1) $y = e^x + x$;
2) $y = x^2$;
3) $y = 3x - \sin x$;
4) $y = \begin{cases} \ln |x|, &x \neq 0 \\ 0, &x = 0 \end{cases}$.

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