
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 $f\left(x\right)=(\frac{1}{x}+a)\ln \left(1+x\right)$.<br/>$(1)$ When $a=-1$, find the equation of the tangent line to the curve $y=f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$;<br/>$(2)$ Determine whether there exist $a$ and $b$ such that the curve $y=f(\frac{1}{x})$ is symmetric with respect to the line $x=b$. If so, find the values of $a$ and $b$; if not, explain the reason;<br/>$(3)$ If $f\left(x\right)$ has extreme values in $\left(0,+\infty \right)$, find the range of values for $a$.

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