
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
Given $ABC$ with $AB = 25$, $BC = 39$, and $AC=42$, and points $D$ and $E$ on $AB$ and $AC$, respectively, such that $AD = 19$ and $AE = 14$, find the ratio of the area of triangle $ADE$ to the area of quadrilateral $BCED$.

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