
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
Let $ABCDE$ be a convex pentagon with $AB \parallel CE, BC \parallel AD, AC \parallel DE, \angle ABC=150^\circ, AB=4, BC=6,$ and $DE = 18.$ Find the ratio between the area of triangle $ABC$ and the area of triangle $AED$, and express it as a fraction $m/n$ where $m$ and $n$ are relatively prime positive integers. Then, find $m+n.$

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