
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 $f(x) = \frac{a - \ln x}{x}$ ($a \in \mathbb{R}$).

(1) Find the extreme values of $f(x)$.

(2) If the graph of the function $f(x)$ has common points with the graph of the function $g(x) = -1$ in the interval $(0, e]$, find the range of the real number $a$.

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