
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
Given point A (4, 0) and a moving point P (x, y) in the first quadrant, with x+y=6, and O as the origin, let the area of triangle OPA be S.  
(1) Find the function expression of S in terms of x;  
(2) Determine the range of values for x;  
(3) When S=6, find the coordinates of point P.

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