
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 trapezoid $EFGH$ be an isosceles trapezoid with bases $\overline{EF}$ and $\overline{GH}$ such that $EF > GH$. A point $Q$ resides within the trapezoid such that line segments from $Q$ to the vertices divide the trapezoid into four triangles. These triangles have areas of $3, 4, 6,$ and $7$ moving clockwise starting from the triangle with base $\overline{GH}$. Determine the ratio $\frac{EF}{GH}$.
A) $\frac{7}{3}$
B) $2$
C) $\frac{5}{2}$
D) $3$

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