
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 $f(x)=mx-α\ln x-m$, $g(x)= \frac {ex}{e^{x}}$, where $m$, $α$ are real numbers.

1. Find the extreme values of $g(x)$;
2. If $m=1$, $α < 0$, and for any $x_{1}$, $x_{2}∈[3,4]$ ($x_{1}≠ x_{2}$), the inequality $|f(x_{2})-f(x_{1})| < | \frac {1}{g(x_{2})}- \frac {1}{g(x_{1})}|$ always holds, find the minimum value of $a$;
3. If $α=2$, and for any given $x_{0}∈(0,e]$, there always exist $t_{1}$, $t_{2}$ ($t_{1}≠ t_{2}$) in the interval $(0,e]$ such that $f(t_{1})=f(t_{2})=g(x_{0})$ holds, find the range of $m$.

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