
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 rectangle is divided such that one vertical side is divided into $k$ congruent segments and the adjacent horizontal side is divided into $l$ congruent segments. The endpoints of one segment from each side are joined to a vertex of the rectangle to form triangle $C$. The opposite sides are each divided into $p$ congruent segments, and the endpoints of one segment from each side are joined to the opposite vertex to form triangle $D$. Calculate the ratio of the area of triangle $C$ to the area of triangle $D$.

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