
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 side \( AC \) of a right isosceles triangle \( ABC \) (where \( \angle BAC = 90^\circ \) and \( AB = BC \)) such that the measure of angle \( DBC \) is \( 45^\circ \). 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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