
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 that the domain of function $f(x)$ is $(0,+\infty)$, if $y=\frac{f(x)}{x}$ is an increasing function on $(0,+\infty)$, then $f(x)$ is called a "first-order ratio increasing function"; if $y=\frac{f(x)}{x^{2}}$ is an increasing function on $(0,+\infty)$, then $f(x)$ is called a "second-order ratio increasing function". Let $\Omega_{1}$ denote the set of all "first-order ratio increasing functions" and $\Omega_{2}$ denote the set of all "second-order ratio increasing functions". Given the function $f(x)=x^{3}-2mx^{2}-mx$, find the range of values of the real number $m$ such that $f(x) \in \Omega_{1}$ and $f(x) \notin \Omega_{2}$.

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