
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
In tetrahedron $ABCD,$
\[\angle ADB = \angle ADC = \angle BDC = 90^\circ.\] Also, let $x = \sin \angle CAD$, $y = \sin \angle CBD$, and $z = \sin \angle BAD$. Express $\cos \angle BAC$ in terms of $x$, $y$, and $z$.

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