
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
Quadrilateral $ABCD$ has right angles at $C$ and $D$, $\triangle BCD \sim \triangle DAB$, and $BC > CD$. There is a point $F$ in the interior of $ABCD$ such that $\triangle BCD \sim \triangle DCF$ and the area of $\triangle BAF$ is $13$ times the area of $\triangle DCF$. What is $\tfrac{BC}{CD}$?

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