
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
Trapezoid $ABCD$ is isosceles with $\overline{AD}$ parallel to $\overline{BC}$. Triangle $EAD$ is equilateral, and lines $\overline{EF}$, $\overline{FG}$, $\overline{GH}$ are all parallel to $\overline{AD}$ (and hence $\overline{BC}$). Suppose $AB = BE = EF = FG = GH$. Express the ratio of the area of triangle $FGH$ to the area of triangle $EAD$.

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