
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 $f(x)=ax^{2}+b(\ln x-x)$ and $g(x)=- \frac {1}{2}x^{2}+(1-b)x$. It is known that the tangent line of the curve $y=f(x)$ at the point $(1,f(1))$ is perpendicular to the line $x-y+1=0$.

(I) Find the value of $a$;

(II) Find the extreme points of the function $f(x)$;

(III) If for any $b\in(1,+\infty)$, there always exist $x_{1}$, $x_{2}\in[1,b]$, such that $f(x_{1})-f(x_{2})-1 > g(x_{1})-g(x_{2})+m$ holds, find the range of the real number $m$.

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