
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 where edges $AB$, $AC$, and $AD$ are mutually perpendicular. Assume that the lengths of these edges are $a$, $b$, and $c$ respectively. If the areas of triangles $ABC$, $ACD$, and $ADB$ are $x$, $y$, and $z$, determine the volume of tetrahedron $ABCD$ in terms of $a$, $b$, $c$, $x$, $y$, and $z$.

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