
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
If $\left(\frac{x^2 - bx + b^2}{ax^2 - c}\right) = \frac{m-1}{m+1}$ has roots that are numerically equal but of opposite signs, and $c=b^2$, find the value of $m$.
**A)** $\frac{b-a}{b+a}$   
**B)** $\frac{b^2-a}{b^2+a}$  
**C)** $\frac{a-1}{a+1}$  
**D)** $\frac{a+1}{a-1}$  
**E)** 1

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