
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 $x = \dfrac{2 + i\sqrt{2}}{3}$ where $i=\sqrt{-1}$. Calculate the value of $\dfrac{1}{x^2+x}$.
A) $\frac{72}{113}$
B) $\frac{63i\sqrt{2}}{113}$
C) $\frac{72 - 63i\sqrt{2}}{113}$
D) $\frac{72 + 63i\sqrt{2}}{113}$

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