
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 the function $f(x)=e^{ax}$ where $a\in\mathbb{R}$.
(I) When $a=-2$, find the maximum value of the function $g(x)=x^{2}f(x)$ in the interval $(0,+\infty)$.
(II) If the function $h(x)=\frac{x^{2}}{f(x)}-1$ has two zeros in the interval $(0,16)$, find the range of the real number $a$.

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