
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 + lnx,

(I) Find the monotonic intervals of the function f(x) when a = 4.

(II) If a ≥ $\frac{5}{2}$, and x₁, x₂ (x₁ < x₂) are two extreme points of the function f(x), find the minimum value of f(x₁) - f(x₂).

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