
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 $\frac{x^2 - (b+1)x}{(a+1)x - c} = \frac{k-2}{k+2}$ has roots which are numerically equal but of opposite signs, the value of $k$ must be:
A) $\frac{-2(a-b)}{a+b-2}$
B) $\frac{2(b-a)}{b+a-2}$
C) $\frac{-2(b-a)}{b+a+2}$
D) $\frac{2(a-b)}{a+b+2}$
E) $\frac{-2(b-a)}{b+a}$

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