
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 $f(x)= x-1+\frac{a}{{{e}^{x}}}$ where $a\in R$ and $e$ is the base of the natural logarithm.

(I) 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 $a$.

(II) When $a=1$, if the line $l$: $y=kx-1$ does not intersect with the curve $y=f(x)$, find the maximum value of $k$.

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