
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 function $f(x) = e^{ax}$ ($a \in \mathbb{R}$).

(I) When $a = -2$, find the maximum value of the function $g(x) = x^2f(x)$ 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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