
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 $f(x)=e^{x}\left( \frac{1}{3}x^{3}-2x^{2}+(a+4)x-2a-4\right)$, where $a\in R$, and $e$ is the base of the natural logarithm.
(1) Find the value of $a$ if the tangent line to the graph of the function $f(x)$ at $x=0$ is perpendicular to the line $x+y=0$.
(2) Find the range of values of $a$ such that the inequality $f(x) < - \frac{4}{3}e^{x}$ holds true on $(-\infty,2)$.
(3) Discuss the number of extreme points of the function $f(x)$.

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