
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 $f\left(x\right)=(\frac{1}{x}+a)\ln \left(1+x\right)$.  
$(1)$ When $a=-1$, find the equation of the tangent line to the curve $y=f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$;  
$(2)$ If the function $f\left(x\right)$ is monotonically increasing on $\left(0,+\infty \right)$, find the range of values for $a$.

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