
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 $f(x)=mx-alnx-m$ and $g(x)= \frac {x}{e^{x-1}}$, where $m$, $a$ are real numbers, and $e$ is the base of the natural logarithm.

(I) Find the extreme values of function $g(x)$;

(II) If $m=1$, $a<0$, and for any $x_1$, $x_2$ in $[3,4]$ ($x_1 \neq x_2$), 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 real number $a$.

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