
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 $f(x)=(a-1)x^{2}+2\ln x$, $g(x)=f(x)-2ax$ ($a\in\mathbb{R}$).  
(1) When $a=0$, find the equation of the tangent line to $f(x)$ at the point $(e,f(e))$.  
(2) If for all $x\in(1,+\infty)$, $g(x) < 0$ always holds, find the range of values for $a$.

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