
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 $f(x) = \frac{a^x}{x} - \ln a$ (where $a > 0$ and $a \neq 1$):
(I) If $a = e$ (where $e = 2.71828\ldots$ is the base of natural logarithms), determine the intervals of monotonicity for the function $y = f(x)$.
(II) Let $g(x) = \frac{e + 1}{ex}$. If $x \in [-1, 0) \cup (0, 1]$ and the curves $y = f(x)$ and $y = g(x)$ intersect at two points, find the range of values of $a$.

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