
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 \( P = (5,5) \), \( Q = (1,1) \), \( R = (6,2) \), and \( S=(x,y) \) lie in the first quadrant and are the vertices of quadrilateral \( PQRS \). The quadrilateral formed by joining the midpoints of \( \overline{PQ} \), \( \overline{QR} \), \( \overline{RS} \), and \( \overline{SP} \) is a square. What is the sum of the coordinates of point \( S \)?
A) 4
B) 5
C) 6
D) 7
E) 8

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