
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 $f(x)=x-1+ \frac {a}{e^{x}}(a\in\mathbb{R})$.  
$(1)$ If the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is parallel to the $x$-axis, find the value of $a$;  
$(2)$ Find the extreme values of the function $f(x)$;  
$(3)$ When $a=1$, if the line $l$: $y=kx-1$ and the curve $y=f(x)$ have no common points, find the maximum value of $k$.

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