
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 $ABCDEF$ be a convex hexagon where $AB \parallel DE$, $BC \parallel EF$, $CD \parallel AF$, $\angle ABC=150^\circ$, $AB=4$, $BC=7$, and $EF=21$. Given that $\triangle ABC$ is similar to $\triangle DEF$, and the ratio of the area of triangle $ABC$ to the area of triangle $DEF$ is $m/n$, where $m$ and $n$ are relatively prime integers, find $m+n$.

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