
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 quadratic function $f(x)=x^{2}+ax+b+1$, the solution set of the inequality $f(x)-(2b-1)x+b^{2} < 1$ is $(b,b+1)$, where $b\neq 0$.  
(I) Find the value of $a$;  
(II) Let $g(x)= \frac {f(x)}{x-1}$, if the function $\varphi(x)=g(x)-k\ln (x-1)$ has an extreme point, find the range of the real number $k$ and the extreme point.

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