
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
If $\left( a+\frac{1}{a} \right)^2=12$, then $a^3+\frac{1}{a^3}$ equals:
A) $24\sqrt{3}$  
B) $18\sqrt{3}$  
C) $12\sqrt{3}$  
D) $6\sqrt{3}$  
E) $30\sqrt{3}$

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