
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: $\sqrt{1 + \left(\frac{x^6 - 2}{3x^3}\right)^2}$.
A) $\frac{\sqrt{x^{12} + 5x^6 + 4}}{3x^3}$  
B) $\frac{x^6 + 2}{3x^3}$  
C) $\frac{\sqrt{x^6 + 1}}{3}$  
D) $\frac{x^3}{\sqrt{3}}$  
E) $\frac{x^3}{3} + \frac{2}{3x^3}$

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