
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 $f(x)=\ln x+ax$ where $a\in \mathbb{R}$.  
$(Ⅰ)$ When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at $x=1$.  
$(Ⅱ)$ Find the intervals where the function $f(x)$ is monotonic.  
$(Ⅲ)$ If there exists $x_{0}$ such that $f(x_{0}) > 0$, find the range of values for $a$.

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