
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
Let the function $f(x)$ have the domain $\mathbb{R}$. If there exists a constant $M > 0$ such that $|f(x)| \leqslant M|x|$ holds for all real numbers $x$, then $f(x)$ is called a "bounded multiple function". Given the following functions:  
1. $f(x)=2x$,  
2. $f(x)=x^{2}+1$,  
3. $f(x)=\sin x+\cos x$,  
4. $f(x)= \frac {x}{x^{2}-x+3}$,  
5. $f(x)$ is an odd function defined on the set of real numbers, and for all $x_{1}$, $x_{2}$, it holds that $|f(x_{1})-f(x_{2})| \leqslant 2|x_{1}-x_{2}|$.  

Among these, the number of "bounded multiple functions" is $\boxed{\text{C: }3}$.

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