
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 that quadrilateral $ABCD$ is a parallelogram in the three-dimensional coordinate system $Oxyz$, with $A(0,1,2)$, $B(-2,0,5)$, and $C(1,-2,4)$.  
$(1)$ Find the coordinates of point $D$.  
$(2)$ Find the area $S$ of the parallelogram $ABCD$.

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