
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  $AB\parallel CE$ ,  $BC\parallel AD$ ,  $AC\parallel DE$ ,  $\angle ABC=120^\circ$ ,  $AB=3$ ,  $BC=5$ , and  $DE=15$ . 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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