
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 \( A = (2,8) \), \( B = (2,2) \), \( C = (6,2) \), and \( D = (a,b) \) lie in the first quadrant and are the vertices of quadrilateral \( ABCD \). The quadrilateral formed by joining the midpoints of \( \overline{AB} \), \( \overline{BC} \), \( \overline{CD} \), and \( \overline{DA} \) is also a square. Determine the sum of the coordinates of point \( D \).
A) 12
B) 14
C) 16
D) 18
E) 20

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