
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
Square PQRV has vertices such that point P is on side AB of square ABCD, with \(AP = 3 \cdot PB\). Find the ratio of the area of square PQRV to the area of square ABCD.
A) \(\frac{1}{64}\)
B) \(\frac{1}{32}\)
C) \(\frac{1}{16}\)
D) \(\frac{1}{8}\)
E) \(\frac{1}{4}\)

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