
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 $f(x)=\frac{1}{2}x^{2}+a\ln x\ (a\in R)$.
(I) If the equation of the tangent line to the graph of the function $f(x)$ at $x=2$ is $y=x+b$, find the values of $a$ and $b$.
(II) If the function $f(x)$ is increasing on $(1,+\infty)$, find the range of values for $a$.

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