
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 points $A(1, -2)$, $B(2, 1)$, $C(3, 2)$, and $D(x, y)$,

$(1)$ Find the coordinates of $3\overrightarrow{AB}-2\overrightarrow{AC}+\overrightarrow{BC}$;  
$(2)$ If points $A$, $B$, $C$, and $D$ form a parallelogram $ABCD$, find the coordinates of point $D$.

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