
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 $f(x)=\frac{1}{2}x^2-ax+(a-1)\ln x$.
(I) Find the value of $a$ such that the tangent line to the function $f(x)$ at the point $(2,f(2))$ is parallel to the line $x+y+3=0$;
(II) Discuss the monotonicity of the function $f(x)$;
(III) For any $x\_1$, $x\_2\in(0,+\infty)$, $x\_1 > x\_2$, if $f(x\_1)-f(x\_2) > x\_2-x\_1$, find the range of the real number $a$.

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