
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
Points $A = (4, 8)$, $B = (2, 2)$, $C = (6, 4)$, and $D = (a, b)$ are vertices of quadrilateral $ABCD$, located in the first quadrant. When connecting the midpoints of $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$, the result is a square. Calculate the sum of coordinates for point $D$.
A) 11
B) 12
C) 13
D) 14
E) 15

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