
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 trapezoid $ABCD$ ($AB \parallel CD$), line $DP$ is drawn bisecting $BC$ at $N$ and meeting $AC$ (extended) at $P$. From vertex $C$, line $CQ$ is drawn bisecting side $AD$ at $M$ and meeting $BD$ (extended) at $Q$. Lines $DP$ and $CQ$ meet at $O$. If the area of trapezoid $ABCD$ is $k$, then the area of the quadrilateral $QPOC$ is equal to
A) $\frac{7k}{16}$ 
B) $\frac{15k}{16}$ 
C) $\frac{17k}{16}$ 
D) $\frac{19k}{16}$

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