
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 $f(x)= \dfrac {ax^{2}+bx}{e^{x}}$ (where $e$ is the base of the natural logarithm, and $a$, $b\in\mathbb{R}$), if $f(x)$ has an extremum at $x=0$, and $x-ey=0$ is the tangent line to the curve $y=f(x)$.
$(1)$ Find the values of $a$ and $b$;
$(2)$ Let $min\{m,n\}$ represent the minimum value between $m$ and $n$. Suppose the function $g(x)=min\{f(x),x- \dfrac {1}{x}\}(x > 0)$, if the function $h(x)=g(x)-cx^{2}$ is an increasing function, find the range of the real number $c$.

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