
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 $f(x)=e^{x}+ax+1$ $(a\in \mathbb{R})$. If $x=0$ is an extremum point of $f(x)$,  
(I) find $a$, and determine the minimum value of $f(x)$ on the interval $[-2,1]$;  
(II) if the inequality $kf'(x) < xe^{x}+1$ holds for any $x > 0$, where $k$ is an integer and $f'(x)$ is the derivative of $f(x)$, find the maximum value of $k$.

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