
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 $B$ and $C$, $\triangle ABC \sim \triangle BCD$, and $AB < BC$. There is a point $E$ on line segment $CD$ such that $\triangle ABC \sim \triangle CED$ and the area of $\triangle AED$ is $9$ times the area of $\triangle CED$. What is $\tfrac{BC}{AB}$?

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