
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 $f(x)=\frac{1}{x}-x+alnx$ has two extreme points $x_{1}$ and $x_{2}$, where $x_{2} \gt x_{1} \gt 0$.  
$(Ⅰ)$ Find the range of $a$.  
$(Ⅱ)$ If $f(x_{2})-f(x_{1})\geqslant ka-3$, find the range of positive real number $k$.

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