
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 $f(x)=e^{x}$ and $g(x)=mx^{2}+ax+b$, where $m$, $a$, $b\in R$, and $e=2.71828…$ is the base of the natural logarithm.
(I) The function $h(x)=xf(x)$, when $a=1$ and $b=0$, if the function $h(x)$ has the same monotonic interval as $g(x)$, find the value of $m$.
(II) Let $F(x)=f(x)-g(x)$. When $a=2$ and $m=0$, if the function $F(x)$ has two distinct zeros on $[-1,2]$, find the range of $b$.

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