
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
A parallelogram $ABCD$ is constructed such that $AB = CD = 14$ and $AD = BC = 18$. Points $P$ and $Q$ on $AB$ and $CD$ respectively, are such that $AP = PD = 7$ and $CQ = QD = 9$. Line segment $PQ$ is drawn, dividing the parallelogram into two smaller parallelograms, $APDQ$ and $PBCQ$. Calculate the ratio of the area of parallelogram $APDQ$ to the area of parallelogram $PBCQ$ and find the sum of the ratio.

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