
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 $f(x)=x- \frac{1}{x}-a\ln x(a∈R)$.
(1) Discuss the monotonic intervals of $f(x)$ when $a > 0$.
(2) Let $g(x)=x- \frac{a}{2}\ln x$. When $f(x)$ has two extreme points $x_{1}$, $x_{2}$, and $x_{1}∈(0,e)$, find the minimum value of $g(x_{1})-g(x_{2})$.

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