
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
If two points are given: M(x<sub>1</sub>, y<sub>1</sub>), N(x<sub>2</sub>, y<sub>2</sub>), then $$MN= \sqrt {(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$$. Given points: A(3, -1), B(-1, 4), C(1, -6), find a point P inside $\triangle ABC$ such that $PA^{2}+PB^{2}+PC^{2}$ is minimized. The coordinates of point P are __________.

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