
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 an isosceles right triangle $ABC$ (where $\angle BAC = \angle BCA = 45^\circ$) such that the measure of angle $DBC$ is $60$ degrees. What is the ratio of the area of triangle $ADB$ to the area of triangle $CDB$? Express your answer as a common fraction in simplest radical form.

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