
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
Given triangle $XYZ$ where $XY=30$, $XZ=15$, the area of the triangle is $90$. Let $M$ be the midpoint of $\overline{XY}$, and let $N$ be the midpoint of $\overline{XZ}$. The angle bisector of $\angle XYZ$ intersects $\overline{MN}$ and $\overline{YZ}$ at $P$ and $Q$, respectively. Calculate the area of quadrilateral $MPQY$.

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