
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 parallelogram with vertices at $(20, 50)$, $(20, 150)$, $(60, 190)$, and $(60, 90)$. A line through the origin cuts this parallelogram into two congruent polygons. Find the slope of that line expressed as a fraction $p/q$, where $p$ and $q$ are coprime positive integers. Determine $p + q$.

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