
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 $ABCD,$
\[\angle ADB = \angle ADC = \angle BDC = 90^\circ.\] If $u = \cos \angle CAD$ and $v = \cos \angle CBD,$ express $\sin \angle ACB$ in terms of $u$ and $v.$

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