
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 $f\left(x\right)=k\left(x-1\right)e^{x}-x^{2}$, where $k\in \mathbb{R}$.  
$(1)$ When $k=1$, find the intervals where the function $f\left(x\right)$ is monotonic.  
$(2)$ If the function $f\left(x\right)$ has two critical points and the minimum value is greater than $-5$, find the range of real numbers for $k$.

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