
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 $EFO$, $FOG$, and $OHC$ have $EF=EO=FO=OH=HC=20$ and $EG=FO=OC=25$. These triangles are arranged to form trapezoid $EGHC$, as shown. Point $Q$ is on side $EG$ such that $OQ$ is perpendicular to $EG$.

 - Point $Z$ is the midpoint of $EH$, and point $W$ is the midpoint of $GC$. When $Z$ and $W$ are joined, the trapezoid is divided into two smaller trapezoids. Calculate the simplified form ratio of the area of trapezoid $EGWZ$ to the area of trapezoid $ZWCH$ and find the sum of the simplified form ratio.

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