
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 $f\left(x\right)=e^{x}+a\ln \left(x+1\right)$, where $a\in \mathbb{R}$.<br/>$(1)$ When $a=-2$, find the equation of the tangent line to the curve $y=f\left(x\right)$ at the point $\left(0,f\left(0\right)\right)$;<br/>$(2)$ If $f\left(x\right)$ has extremum in its domain, find the range of values for $a$;<br/>$(3)$ If $f\left(x\right)\geqslant 1-\sin x$ always holds, find the value of $a$.

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