
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
Let \( x=\frac{1+i\sqrt{3}}{2} \) where \( i=\sqrt{-1} \). Calculate \( \frac{1}{x^3-x} \).
**A)** \( \frac{-6}{39} \)
**B)** \( \frac{-6+i\sqrt{3}}{39} \)
**C)** \( -2 + i\sqrt{3} \)
**D)** \( -1 \)

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