
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 $f(x)=2\ln{x} - \frac{1}{2}ax^2+(2-a)x$ where $a\in\mathbb{R}$.
(I) Discuss the monotonicity of the function $f(x)$;
(II) If for all $x_1, x_2 \in (0, +\infty)$ and $x_1 < x_2$, there exists a positive real number $x_0$ such that $f(x_2)-f(x_1)=f'(x_0)(x_2-x_1)$, determine the relationship between $f'\left(\frac{x_1+x_2}{2}\right)$ and $f'(x_0)$, and provide proof.

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