
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
Let the function $f(x)=a\ln x+ \frac {1-a}{2}x^{2}-bx\ (a\neq 1)$, and the slope of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is $0$,

$(1)$ Find $b$;  
$(2)$ If there exists $x_{0}\geqslant 1$ such that $f(x_{0}) < \frac {a}{a-1}$, find the range of values for $a$.

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