
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 triangle $ABC$, $AB = 24$, $BC = 45$, and $AC = 48$. Points $D$ and $E$ are on $AB$ and $AC$ respectively, such that $AD = 18$ and $AE = 16$. There exists a point $F$ on $BC$ such that $DF \parallel BE$. Calculate the ratio of the area of $\triangle ADE$ to the area of quadrilateral $BCED$.
**A)** $\frac{1}{12}$  
**B)** $\frac{1}{15}$  
**C)** $\frac{1}{18}$  
**D)** $\frac{1}{20}$

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