
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 three points \(A\), \(B\), and \(C\) on a plane, which are not collinear, find a point \(M\) on the line passing through points \(B\) and \(C\) such that the sum of the squares of its distances from points \(A\), \(B\), and \(C\) is minimized.

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