
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 the trapezoid $ABCD$ have parallel bases $\overline{AB}$ and $\overline{CD}$ with $AB>CD$. A point $P$ inside the trapezoid connects to the vertices, dividing the trapezoid into four triangles. The areas of these triangles from the triangle with base $\overline{CD}$ moving clockwise are $4, 6, 5,$ and $7$. If the total height of the trapezoid from $\overline{CD}$ to $\overline{AB}$ is known to be $8$, find the ratio $\frac{AB}{CD}$.

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