
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
Let \(ABCD\) be a tetrahedron with \(AB=2b\), \(AC=2c\), and \(AD=2d\) where \(b, c, d\) are positive, and edges \(AB, AC, AD\) are mutually perpendicular. Let the areas of triangles \(ABC\), \(ACD\), and \(ADB\) be \(2x\), \(2y\), and \(2z\) respectively. Find the area of triangle \(BCD\).

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