
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
Consider a dartboard painted over a rectangular clock face with the dimensions ratio of length to width being 2:1, using only the 3, 6, 9, and 12 "hour positions" as boundaries. Determine the ratio of the area of one of the rectangle cut by the 3 and 9 o'clock marks from the center (let's denote this as $p$), and the area of one of the triangles formed by the intersections at 12 and 6 o'clock with one of the corners (let's denote this as $r$). Calculate $\frac{p}{r}$.
A) $\frac{1}{2}$
B) $2$
C) $4$
D) $8$

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