
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 $f(x)=ax-a\ln x-\frac{e^x}{x}$.  
$(1)$ If the inequality $f(x) < 0$ holds for all $x$, find the range of real number $a$.  
$(2)$ If the function $y=f(x)$ has three distinct critical points $x_{1}$, $x_{2}$, $x_{3}$, and $f(x_{1})+f(x_{2})+f(x_{3})\leqslant 3e^{2}-e$, find the range of real number $a$.

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