
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
Point $D$ lies on hypotenuse $AC$ of right triangle $ABC$ such that $\angle ABC = 90^\circ$ and the measure of $\angle DBC$ is $45$ degrees. Side $AB$ measures $a$ units. What is the ratio of the area of triangle $ADB$ to the area of triangle $CDB$?

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