
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
Consider the function
$$
f(x) = 4\ln x - \frac{1}{2}ax^2 + (4-a)x \quad (a\in R).
$$

(I) Discuss the monotonicity of $f(x)$.
(II) If the function $f(x)$ has an extremum, then for any $0 < x_1 < x_2$, there exists a positive real number $x_0$ such that
$$
f(x_1) - f(x_2) = f'(x_0)(x_1 - x_2).
$$
Determine the relationship between $x_1 + x_2$ and $2x_0$ and provide a proof.

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