
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
The convex quadrilateral $ABCD$ has equal angles at vertices $A$ and $B$, and the angle at vertex $C$ is a right angle. The side $AD$ is perpendicular to the diagonal $BD$. The length of side $BC$ is equal to the length of side $CD$. How many times is this common length the length of side $AD$?

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