
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
In a different configuration, triangles $ABC$ and $ABD$ are right triangles with $C$ and $D$ on the same side of $\overline{AB}$. Triangle $ABC$ has a right angle at $C$, $AC=4$ and $BC=3$. Triangle $ABD$ has a right angle at $A$ and $AD=15$. The line through $D$ parallel to $\overline{AC}$ meets $\overline{CB}$ extended at $E$. Find the ratio $\frac{DE}{DB}$ and express the sum of the numerator and denominator in simplest form.

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