
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 positioned with its lower left corner at the origin (0,0) and its upper right corner at coordinates (a, b). The bottom side is divided into \(p\) segments on the left half and \(q\) segments on the right half, where \(p+q=n\). The left vertical side is uniformly divided into \(m\) segments. A line is drawn from the center of the rectangle to a point dividing the bottom left half into \(p\) segments forming triangle \(C\), and another line is drawn to a point dividing the left side into \(m\) segments forming triangle \(D\). Determine 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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