
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 $FBCDE$ be a convex pentagon where $FB \parallel DE$, $BC \parallel FD$, $BD \parallel CE$, $\angle FBC = 120^\circ, FB = 4, BC = 7,$ and $CE = 21$. Find the ratio of the area of triangle $FBC$ to the area of triangle $CBD$ and express it as a fraction of relatively prime integers $m/n$ then calculate $m+n$.

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