
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
In quadrilateral $ABCD$, $E$ is the midpoint of diagonal $AC$. One of the diagonals, $BD$, intersects $AC$ at $M$. Let $N$ be the midpoint of diagonal $BD$. Let the area of $△MNE$ be $k$ times the area of quadrilateral $ABCD$. Find $k$.
A) $\frac{1}{6}$
B) $\frac{1}{8}$
C) $\frac{1}{9}$
D) $\frac{1}{12}$
E) $\frac{1}{16}$

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