
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
When simplified, $\sqrt{1+ \left(\frac{x^6-1}{2x^3}\right)^2}$ equals:
A) $\frac{x^3}{3} + \frac{1}{2x^3}$    
B) $\frac{x^3}{2} + \frac{1}{2x^3}$    
C) $\frac{x^6}{2} + \frac{1}{x^3}$    
D) $\frac{x^6 + 1}{2x^3}$    
E) $\frac{3x^3}{2} + \frac{2}{x^3}$

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