
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
In the 19th century, Danish mathematician Kierkegaard made outstanding contributions to mathematical analysis, especially in the concavity and convexity of functions and inequalities. It is defined that the derivative of a function $f(x)$ on the interval $(a, b)$ is denoted as $f'(x)$, and the derivative of $f'(x)$ on the interval $(a, b)$ is denoted as $f''(x)$. If $f''(x) < 0$ holds for all $x$ in $(a, b)$, then the function $f(x)$ on $(a, b)$ is called a "strictly convex function." If the function $f(x) = e^x - x\ln x - \frac{m}{2}x^2$ is a "strictly convex function" on $(1, 4)$, then the range of $m$ is ____.

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