
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 $f(x)=\frac{e^x}{x}+a(x-\ln x)$ (where $e$ is the base of the natural logarithm),

(1) When $a > 0$, determine the intervals of monotonicity for $f(x)$;  
(2) If the function $f(x)$ has three distinct extreme points in the interval $x \in \left( \frac{1}{2},2 \right)$, find the range of the real number $a$.

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