
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
Solve the quadratic equation $(x-h)^2 + 4h = 5 + x$ and find the sum of the squares of its roots. If the sum is equal to $20$, what is the absolute value of $h$?
**A)** $\frac{\sqrt{22}}{2}$  
**B)** $\sqrt{22}$  
**C)** $\frac{\sqrt{44}}{2}$  
**D)** $2$  
**E)** None of these

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