
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 $f(x)=xe^x-ax$ (where $a\in \mathbb{R}$ is a constant, and $e$ is the base of the natural logarithm),

(I) When $f(x) > 0$, find the range of real numbers $x$;

(II) When $a=2$, find the minimum positive integer $k$ such that $f(x)+k > 0$.

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