
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 $\triangle ABC$, $\angle C = 90^\circ$ and $AB = 10$. Square $ABXY$ is constructed outside of the triangle along $AB$. A rectangle, $ABPQ$, is constructed atop hypotenuse $AB$, where $BP = 2AB$ and $AP = \frac{1}{2}AB$. Determine the area of rectangle $ABPQ$.
A) 50 square units
B) 100 square units
C) 150 square units
D) 200 square units

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