
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 a scalene trapezoid with parallel bases $\overline{AB}$ and $\overline{CD}$ where $AB>CD$. A point $P$ inside the trapezoid connects to vertices, dividing the trapezoid into four triangles. The areas of these triangles, starting with the triangle with base $\overline{CD}$ and moving clockwise, are $3, 5, 7,$ and $10$. Determine the ratio $\frac{AB}{CD}$.

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