
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 $f(x)=\ln x-ax^2+(2-a)x$.

(Ⅰ) Discuss the monotonicity of the function $f(x)$;

(Ⅱ) Let $g(x)= \frac{x}{e^x} -2$, for any given $x_0 \in (0,e]$, the equation $f(x)=g(x_0)$ has two different real roots in $(0,e]$. Find the range of the real number $a$ (where $a \in \mathbb{R}$, $e=2.71828…$ is the base of the natural logarithm).

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