
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 $PQRST$ be a convex pentagon with $PQ \parallel ST, QR \parallel PS, PT \parallel RS, \angle PQR=120^\circ, PQ=4, QR=6,$ and $RS = 18.$ Given that the ratio between the area of triangle $PQR$ and the area of triangle $QTS$ is $x/y,$ where $x$ and $y$ are relatively prime positive integers, find $x+y.$

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