
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 positive constant $M$ independent of $x$ such that $|f(x)| \leq M|x|$ for all real numbers $x$, then $f(x)$ is called a bounded functional. Among the functions:
- $f(x) = -3x$
- $f(x) = x^2$
- $f(x) = \sin^2 x$
- $f(x) = 2^x$
- $f(x) = x\cos x$

Identify the ones that are bounded functionals.

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