
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 \(AB \parallel CE\), \(BC \parallel AD\), \(AC \parallel DE\), \(\angle ABC = 100^\circ\), \(AB = 4\), \(BC = 6\), and \(DE = 18\). Given that the ratio between the area of triangle \(ABC\) and the area of triangle \(EBD\) is \(m/n\), where \(m\) and \(n\) are relatively prime positive integers, find \(m+n\).

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