
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 $f(x)=e^{x}-a\ln x$ ($a\in\mathbb{R}$).  
$(1)$ Find the equation of the tangent line to the function $f(x)$ at the point $(1,f(1))$.  
$(2)$ When $a=-1$, if the inequality $f(x) > e+m(x-1)$ holds for any $x\in(1,+\infty)$, find the range of the real number $m$.

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