
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 $(4,0), (6,0), (9,0),$ and $(15,0)$ lie on lines $DA, CB, AB$, and $DC$, respectively. What is the sum of the coordinates of the center of the square $ABCD$?
**A)** $1.2$
**B)** $2.4$
**C)** $3.6$
**D)** $4.8$
**E)** $6.0$

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