
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 $f(x)=\ln x+ \frac{m}{e^{x}}-1(m∈R)$, where $e=2.718…$ is an irrational number.
(1) If the function $f(x)$ has two extreme points, find the range of $m$.
(2) If the function $g(x)=(x-2)e^{x}- \frac{1}{3}mx^{3}+ \frac{1}{2}mx^{2}$ has three extreme points, denote the smallest one as $x_{1}$ and the largest one as $x_{2}$. If the maximum value of $\frac{x_{1}}{x_{2}}$ is $\frac{1}{e}$, find the minimum value of $x_{1}+x_{2}$.

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