
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 $f(x) = x^2 - ax + 2\ln x$ (where $a$ is a real number),
(1) Find the intervals of monotonicity for $f(x)$;
(2) If $2(e + \frac{1}{e}) < a < \frac{20}{3}$, and $f(x)$ has two extreme points $x_1$, $x_2$ ($x_1 < x_2$), find the range of values for $f(x_1) - f(x_2)$. (Here $e$ is the base of the natural logarithm).

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