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

(1) Find the value of $b$;  
(2) If there exists $x \in [1, +\infty)$ such that $f(x) < \frac{a}{a-1}$, find the range of values for $a$.

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