
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 $ABCD$ be an isosceles trapezoid with $AB$ and $CD$ as parallel bases, and $AB > CD$. A point $P$ inside the trapezoid connects to the vertices $A$, $B$, $C$, $D$, creating four triangles. The areas of these triangles, starting from the triangle with base $\overline{CD}$ moving clockwise, are $3$, $4$, $6$, and $7$. Determine the ratio $\frac{AB}{CD}$.
- **A**: $2$
- **B**: $\frac{5}{2}$
- **C**: $\frac{7}{3}$
- **D**: $3$
- **E**: $\sqrt{5}$

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