
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 $f(x) = (x-k)e^x$,  
(I) Determine the intervals of monotonicity for $f(x)$;  
(II) Find the minimum value of $f(x)$ on the interval $[0, 1]$;  
(III) When $k \leq 1$, it is always true that $f(x) > k^2 - 2$ on the interval $[0, 1]$. Find the range of values for $k$.

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