
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
Consider the quadratic equation $x^2 - 4hx = 8$. If the sum of the squares of the roots of this equation is $18$, find the value of $h$.
**A)** $\textstyle \frac{\sqrt{2}}{4}$  
**B)** $-\textstyle \frac{\sqrt{2}}{4}$  
**C)** $\textstyle \frac{1}{2}$  
**D)** $-\textstyle \frac{1}{2}$  
**E)** $0$

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