
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 $FGHIJ$ be a convex pentagon with $FG \parallel IJ, GH \parallel FI, GI \parallel HJ, \angle FGH = 120^\circ, FG = 4, GH = 6,$ and $HJ = 18.$ Given that the ratio between the area of triangle $FGH$ and the area of triangle $GHI$ is $p/q,$ where $p$ and $q$ are relatively prime positive integers, find $p+q.$

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