
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
For the function $f(x)$, if there exists $x \in \mathbb{R}$ such that $f(x) = x$ holds, then $x$ is called a fixed point of $f(x)$. It is known that the function $f(x) = ax^2 + (b+1)x + b - 1$ ($a \neq 0$).
(1) When $a=1$, $b=-2$, find the fixed points of $f(x)$;
(2) If for any real number $b$, the function $f(x)$ always has two distinct fixed points, find the range of values for $a$.

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