
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 $f(x)=x$, then $x$ is called the "fixed point" of $f(x)$. Given $f(x)=ax^2+(b+1)x+b-2$ (where $a \neq 0$),  
(1) If $a=2$ and $b=-2$, find the fixed points of $f(x)$;  
(2) If $f(x)$ has two distinct fixed points, determine the range of the real number $a$.

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