
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 $x = \frac{1 + i\sqrt{3}}{3}$. Compute the value of $\frac{1}{x^2 + x}$.
**A)** $\frac{5}{76} - \frac{49i\sqrt{3}}{152}$
**B)** $\frac{9}{76} - \frac{45i\sqrt{3}}{76}$
**C)** $\frac{11}{76} - \frac{3i\sqrt{3}}{76}$
**D)** $\frac{7}{76} - \frac{35i\sqrt{3}}{152}$

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