
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 $(12,50)$, $(12,120)$, $(30,160)$, and $(30,90)$. A line through the origin cuts this parallelogram into two congruent polygons. Find the slope of the line in the form $m/n$, where $m$ and $n$ are coprime integers, and determine the sum $m+n$.

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