
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
Let $kr$ and $ks$ be the roots of the modified equation $ax^2+kcx+b=0$. Determine the value of $\frac{1}{(kr)^2}+\frac{1}{(ks)^2}$.
- **A)** $\frac{(kc)^2 - 4ab}{b^2}$
- **B)** $\frac{k^2c^2 - 2ab}{b^2}$
- **C)** $\frac{b^2 - 4ac}{c^2}$
- **D)** $\frac{(kc)^2 - 2ab}{c^2}$

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