
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 $f(x) = (x \ln x + ax + a^2 - a - 1)e^x$, where $a \geq -2$.
(I) If $a=0$, find the monotonic intervals of $f(x)$;
(II) Discuss the number of extreme points of the function $f(x)$ in the interval $(\frac{1}{e}, +\infty)$;
(III) Determine whether there exists an $a$ such that the graph of the function $f(x)$ is tangent to the $x$-axis in the interval $(\frac{1}{e}, +\infty)$. If it exists, find all the values of $a$; if not, explain the reason.

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