
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 functions $f(x) = \ln x - ax^2 + (2-a)x$ and $g(x) = \frac{x}{e^x} - 2$.
(1) Find the extreme values of the function $f(x)$.
(2) If for any given $x_0 \in (0, e]$, the equation $f(x) = g(x_0)$ always has two distinct real roots in $(0, e]$, find the range of the real number $a$.

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