
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 $f(x)=e^{x}+ax-e$, where $a\in \mathbb{R}$ (Note: $e=2.718281\ldots$ is the base of the natural logarithm). Find:

$(Ⅰ)$ When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$.

$(Ⅱ)$ If $f(x)$ has only one critical point, find the range of real numbers for $a$.

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