
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 domain $\mathbb{R}$, if there exists a constant $m > 0$ such that for any $x \in \mathbb{R}$, $|f(x)| \leqslant m|x|$, then $f(x)$ is called an $F$ function. Consider the following functions:

1. $f(x) = x^{2}$;
2. $f(x) = \sin x + \cos x$;
3. $f(x) = \frac{x}{x^{2} + x + 1}$;
4. $f(x)$ is an odd function defined on $\mathbb{R}$, and it satisfies $|f(x_{1}) - f(x_{2})| \leqslant 2|x_{1} - x_{2}|$ for all real numbers $x_{1}, x_{2}$.

The numbers of the functions that are $F$ functions are $\boxed{\text{3, 4}}$.

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