
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
Square ABCD lies in the first quadrant. Points (4,0), (6,0), (8,0), and (14,0) lie on lines AD, BC, AB, and CD, respectively. Determine the sum of the coordinates of the center of the square ABCD.

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