
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
A function $f(x)$ defined on $\mathbb{R}$ is called an "H function" if for any two distinct real numbers $x\_1, x\_2$, it satisfies $x\_1f(x\_1) + x\_2f(x\_2) > x\_1f(x\_2) + x\_2f(x\_1)$. Determine which of the following functions are "H functions": ① $y = -x^3 + x + 1$; ② $y = 3x - 2(\sin x - \cos x)$; ③ $y = e^x + 1$; ④ $f(x) = \begin{cases} \ln|x|, & x \neq 0 \\ 0, & x = 0 \end{cases}$.

List the serial numbers of all "H functions" as the answer.

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