
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) = x^2 + ax - (a + 2)lnx, x ∈ (0, +∞), where a is a real number.
(1) If a = 1, find the monotonic intervals and the extreme values of f(x);
(2) Let g(x) = f(x) + (a + 4)lnx - (a + 2b - 2)x, and g(x) has two extreme points x1, x2 (x1 < x2). If b ≥ 1 + $\frac {4 \sqrt {3}}{3}$, find the minimum value of g(x1) - g(x2).

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