
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 \(A = (2,8)\), \(B = (2,2)\), and \(C = (6,2)\) lie in the first quadrant and are vertices of triangle \(ABC\). Point \(D=(a,b)\) is also in the first quadrant, and together with \(A\), \(B\), and \(C\), forms quadrilateral \(ABCD\). The quadrilateral formed by joining the midpoints of \(\overline{AB}\), \(\overline{BC}\), \(\overline{CD}\), and \(\overline{DA}\) is a square. Additionally, the diagonal of this square has the same length as the side \(\overline{AB}\) of triangle \(ABC\). Find the sum of the coordinates of point \(D\).
A) 12
B) 14
C) 15
D) 16
E) 18

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