
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
Simplify the expression \(\sqrt{1 + \left(\frac{x^4 + 1}{2x^2}\right)^2}\), assuming \( x^2 \neq 1 \).
**A)** \(\frac{x^2}{2} + \frac{1}{2x^2}\)  
**B)** \(\frac{\sqrt{x^8 + 2x^4 + 1}}{2x^2}\)  
**C)** \(\frac{\sqrt{x^8 + 6x^4 + 1}}{2x^2}\)  
**D)** \(\frac{x^4}{2x^2} + \frac{1}{2}\)  
**E)** \(\frac{x^4+1}{2x^2}\)

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