
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 $g(x)=a\ln x+ \frac{1}{2}x^{2}+(1-b)x$.
(1) If the equation of the tangent line at the point $(1,g(1))$ is $8x-2y-3=0$, find the values of $a$ and $b$.
(2) If $b=a+1$, and $x\_1$, $x\_2$ are the two extreme points of the function $g(x)$, compare $-4$ with $g(x\_1)+g(x\_2)$.

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