
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
Rectangle $ABCD$ lies in the first quadrant, with the horizontal side $AB$ placed along the x-axis. Points $(6,0)$ and $(10,0)$ are located on line $AB$, and point $(2,0)$ is on line $AD$. Point $(2,y)$, where $y > 0$, is on line $CD$. Determine the sum of the coordinates of the center of rectangle $ABCD$.
A) 12  
B) $9$  
C) $8.5$  
D) $8 + \frac{y}{2}$  
E) None of the above

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