
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
If the function $f(x) = \frac{1}{12}x^{4} - \frac{m}{6}x^{3} - \frac{3}{2}x^{2}$ is a "convex function" on the interval $(1,3)$, and $f''(x) < 0$ always holds on the interval $(1,3)$, determine the range of the real number $m$.

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