
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 $f(x)=x-a\ln x-1$ $(a\in \mathbb{R})$ and $g(x)=xe^{1-x}$,

(I) Find the extreme value of $g(x)$;

(II) Let $a=2$, the function $h(x)=x^{3}+x^{2}\left[f'(x)+ \frac {m}{2}\right]$ is not monotonic in the interval $(2,3)$. Find the range of the real number $m$;

(III) When $a < 0$, for any $x_{1}, x_{2} \in [3,4]$ $(x_{1} \neq x_{2})$, if inequality $|f(x_{2})-f(x_{1})| < \left| \frac {1}{g(x_{2})}- \frac {1}{g(x_{1})}\right|$ always holds, find the minimum value of $a$.

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