
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 $\triangle XYZ$, the given area is $15$ square units. Points $P, Q$, and $R$ lie on sides $XY, YZ$, and $ZX$. Lengths $XP = 3$, $PY = 6$, and it is known that triangles $\triangle XPQ$ and quadrilateral $PYRQ$ have equal areas. Determine the area of $\triangle XPQ$.
**A)** $\frac{15}{2}$  
**B)** $\frac{5}{3}$  
**C)** $\frac{15}{9}$  
**D)** $\frac{15}{27}$  
**E)** $\frac{3}{2}$

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