
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
Segments \(AD\), \(BD\), and \(CD\) are pairwise perpendicular. It is known that the area of triangle \(ABC\) is \(S\), and the area of triangle \(ABD\) is \(Q\). Find the area of the orthogonal projection of triangle \(ABD\) onto the plane \(ABC\).

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