
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 where $AB \parallel DE, BC \parallel AE, BD \parallel CE, \angle ABC=100^\circ, AB = 4, BC = 6,$ and $DE = 18.$ Find the ratio between the area of triangle $ABC$ and the area of triangle $CDE$, expressed as a reduced fraction $m/n$ where $m$ and $n$ are relatively prime integers and find $m+n.$

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