
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 $f(x) = \frac{ax^2 + bx + c}{e^x}$ $(a > 0)$, its derivative $y = f′(x)$ has two zero points at $-3$ and $0$.

(1) Find the monotonic intervals of $f(x)$;
(2) If the minimum value of $f(x)$ is $-e^{3}$, find the maximum value of $f(x)$ on the interval $[-5, +\infty)$.

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