
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

Given the vertices of a tetrahedron $A(2, -1, 2)$, $B(5, 5, 5)$, $C(3, 2, 0)$, and $D(4, 1, 4)$, calculate the following:
1) The volume of the tetrahedron;
2) The height of the tetrahedron drawn from vertex $D$;
3) The angle between edge $AD$ and the face $ABC$.

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