
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 $f(x)=(ax^{2}+bx+a-b)e^{x}- \frac {1}{2}(x-1)(x^{2}+2x+2)$, where $a\in\mathbb{R}$, and the curve $y=f(x)$ is tangent to the x-axis at the origin $O$.  
$(1)$ Find the values of the real numbers $a$ and $b$;  
$(2)$ If $f(x)\cdot(x^{2}+mx-n)\geqslant 0$ always holds, find the value of $m+n$.

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