
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 $P = (2,7)$, $Q = (3,2)$, and $R = (6,4)$ lie in the first quadrant and are vertices of quadrilateral $PQRS$. The quadrilateral formed by joining the midpoints of lines $\overline{PQ}$, $\overline{QR}$, $\overline{RS}$, and $\overline{SP}$ is a square. What is the sum of the coordinates of point $S$?
A) 7
B) 10
C) 12
D) 14
E) 16

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