
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 functions $f(x)=kxe^{x}- \frac {x^{2}}{2}-x$ and $g(x)=ke^{x}-x$, where $k\in\mathbb{R}$.
(1) When $k=1$, find the monotonic intervals of the function $f(x)$ and determine its extreme values.
(2) If the function $F(x)=f(x)-g(x)$ has two zeros, find the range of $k$.

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