
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 $f(x)=ax-\frac{a}{x}-4\ln x$ has two extreme points $x_1$ and $x_2$ satisfying $x_1 < x_2$ and $1 < x_2 < e$, where $e$ is the base of the natural logarithm.

(1) When $a=1$, find the value of $x_1^2+x_2^2$;

(2) Find the range of $f(x_2)-f(x_1)$.

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