
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 triangle $XYZ$ where $XY=60$ and $XZ=15$, the area of the triangle is given as $225$. Let $W$ be the midpoint of $\overline{XY}$, and $V$ be the midpoint of $\overline{XZ}$. The angle bisector of $\angle YXZ$ intersects $\overline{WV}$ and $\overline{YZ}$ at points $P$ and $Q$, respectively. Determine the area of quadrilateral $PQYW$.
A) $110$ 
B) $120$ 
C) $123.75$ 
D) $130$

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