
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 derivative of the function $y=f\left(x\right)$ on the interval $\left(a,b\right)$ be ${f'}\left(x\right)$, and the derivative of ${f'}\left(x\right)$ on the interval $\left(a,b\right)$ be $f''\left(x\right)$. If $f''\left(x\right) \lt 0$ holds for all $x$ in the interval $\left(a,b\right)$, then the function $f\left(x\right)$ on the interval $\left(a,b\right)$ is called a "convex function". Given $f(x)=\frac{1}{{12}}{x^4}-\frac{m}{6}{x^3}-\frac{3}{2}{x^2}$ is a "convex function" on $\left(1,3\right)$, the range of real number $m$ is ______.

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