
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) = x² + ax + 2lnx, where 'a' is a constant.
(I) Find the range of 'a' for which f(x) is a monotonic function in its domain.
(II) If f(x) has two extreme points x₁ and x₂, and $|x_{1} - x_{2}| \leq \frac{3}{2}$, find the maximum value of $|f(x_{1}) - f(x_{2})|$.

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