
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 $f(x)=\dfrac{a(x-1)+b{e}^{x}}{{e}^{x}}(a\ne 0)$.

$(1)$ When $a=-1$, $b=0$, find the extremum of the function $f(x)$;

$(2)$ When $b=1$, if the function $f(x)$ has no zeros, find the range of the real number $a$.

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