
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
Three congruent isosceles triangles $EFO$, $OFG$ and $OGH$ have $EF=EO=OG=GH=12$ and $FG=EH=OH=18$. These triangles are arranged to form trapezoid $EFGH$. Point $Q$ is on side $FG$ such that $OQ$ is perpendicular to $FG$. 

Point $Z$ is the midpoint of $EF$ and point $W$ is the midpoint of $GH$. When $Z$ and $W$ are joined, the trapezoid is divided into two smaller trapezoids. Calculate the ratio of the area of trapezoid $EFWZ$ to the area of trapezoid $ZWGH$ in simplified form and find the sum of the integers in this ratio.

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