
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
Let points $A = (4,10)$, $B = (2,2)$, and $C = (6,4)$ lie in the first quadrant on the Cartesian plane. Point $D=(a,b)$ along with $A$, $B$, and $C$, forms quadrilateral $ABCD$, where $\overline{ABCD}$ are the vertices. A quadrilateral drawn by connecting the midpoints of $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$ results in a square. Determine the sum of the coordinates of point $D$.
A) 10
B) 12
C) 14
D) 16
E) 18

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