
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 $f(x)=b\ln x$.
(I) When $b=1$, find the range of values of $a$ such that the function $F(x)=f(x)+ax^{2}-x$ is an increasing function over its domain.
(II) If there exists $x_{0}$ in $[1,e]$ such that $x_{0}-f(x_{0}) < - \frac {1+b}{x_{0}}$, find the range of values of $b$.

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