
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 $f(x)=\ln x+ax^{2}$ and $g(x)= \frac {1}{x}+x+b$, and the line $y=- \frac {1}{2}$ is a tangent line of the function $f(x)$.
(I) Find the value of $a$;
(II) For any $x_{1}∈[1, \sqrt {e}]$, there exists $x_{2}∈[1,4]$, such that $f(x_{1})=g(x_{2})$, find the range of values of $b$.

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