
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 $a \in \mathbb{R}$.

(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) Find the extreme values of the function $f(x)$.

(III) 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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