
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
Find the absolute value of $k$ if the sum of the squares of the roots of the equation $x^2 - 4kx + 1 = 0$ is $17$.
**A)** $\frac{\sqrt{17}}{4}$  
**B)** $\frac{\sqrt{19}}{4}$  
**C)** $\frac{\sqrt{21}}{4}$  
**D)** $\frac{\sqrt{23}}{4}$

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