
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 \( EF=EO=OG=GH=15 \) and \( FG=EO=OH=18 \). These triangles are arranged to form trapezoid \( EFGH \), as shown. 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. Find the ratio of the area of trapezoid \( EFZW \) to the area of trapezoid \( ZWGH \) in simplified form, and calculate \( r+s \) where the ratio is \( r:s \).

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