
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) = xlnx - $\frac{a}{2}$x^2 has two different extreme points x1, x2 (x1 < x2).
(I) Find the range of the real number a;
(II) Let g(x) = f(x) - $\frac{x_2}{2}$, discuss the number of zeros of the function g(x).

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