
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
There are two points A(-1,0) and B(1,0) on a plane. Point P lies on the circumference of the circle $(x-3)^2+(y-4)^2=4$. Find the coordinates of point P for which the sum $AP^2+BP^2$ is minimized.

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