
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 $f(x)=e^{x}+(1-a)x-\ln(ax)$ where $(a>0)$.  
$(1)$ When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$.  
$(2)$ If $f(x)\geqslant 0$ for all $x>0$, find the range of positive values for $a$.

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