
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 $f(x)=ae^{x}-x+\ln a-2$.  
$(Ⅰ)$ If $x=0$ is a critical point of $f(x)$, find the minimum value of $f(x)$.  
$(Ⅱ)$ If the function $g(x)=f(x)+x-\ln(x+2)$ has two zeros, find the range of values for $a$.

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