
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 $XY = 80$ and $XZ = 20$, the triangle has an area of $240$. Let $P$ be the midpoint of $\overline{XY}$, and let $Q$ be the midpoint of $\overline{XZ}$. The angle bisector of $\angle XYZ$ intersects $\overline{PQ}$ and $\overline{YZ}$ at $R$ and $S$ respectively. What is the area of quadrilateral $RSYP$?
A) 150
B) 160
C) 170
D) 177.5
E) 182.5

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