
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 $f(x)=x^{2}+ax-\ln x(a\in R,a$ is a constant$)$
(1) When $a=-1$, find the minimum value of $b$ such that the equation $f(x)= \frac {b}{x}$ has real roots;
(2) Let $F(x)=f(x)\cdot e^{-x}$, find the range of $a$ such that $F(x)$ is a monotonic function on the interval $(0,1]$.

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