
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 \(A B C D\) be a tetrahedron such that edges \(A B\), \(A C\), and \(A D\) are mutually perpendicular. Let the areas of triangles \(A B C\), \(A C D\), and \(A D B\) be denoted by \(x\), \(y\), and \(z\), respectively. In terms of \(x\), \(y\), and \(z\), find the area of triangle \(B C D\).

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