
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 $f\left(x\right)=e^{x}-ax+b\left(a,b\in R\right)$.
1. If the local minimum of $f\left(x\right)$ at $x=0$ is $2$, find the values of $a$ and $b$.
2. Let $g\left(x\right)=f\left(x\right)+\ln \left(x+1\right)$. If $g\left(x\right)\geqslant 1+b$ for $x\geqslant 0$, find the range of values for $a$.

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