
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 height of the triangular pyramid \(ABCD\) dropped from vertex \(D\) passes through the point of intersection of the heights of triangle \(ABC\). Additionally, it is known that \(DB = 3\), \(DC = 2\), and \(\angle BDC = 90^{\circ}\). Find the ratio of the area of face \(ADB\) to the area of face \(ADC\).

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