
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
Given a function $f(x)$ with the domain of $\mathbb{R}$, if there exists a constant $k$ such that $|f(x)| \leqslant \frac{k}{2017}|x|$ holds for all real numbers, then the function $f(x)$ is called an "expected function". Consider the following functions:  
1. $f(x)=x^{2}$
2. $f(x)=xe^{x}$
3. $f(x)= \frac{x}{x^{2}-x+1}$
4. $f(x)= \frac{x}{e^{x}+1}$  

Among these functions, the ones that are "expected functions" are __________. (Write down all the correct option numbers)

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