
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 \( y=f(x) \), if there exists \( x_0 \in \mathbb{R} \) such that \( f(x_0) = x_0 \) holds, then \( x_0 \) is called the fixed point of \( f(x) \). Given the function \( f(x) = ax^2 + (b+1)x + b - 1 (a \neq 0) \):

   \( (1) \) When \( a=1 \), \( b=5 \), 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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