
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 $f(x) = ax^2 + bx + (b-1)$ ($a \neq 0$):

(1) When $a=1$ and $b=-2$, find the zeros of the function $f(x)$.

(2) If for any real number $b$, the function always has two distinct zeros, find the range of values for the real number $a$.

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