
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
Consider the set of all points \(P\) such that the sum of the distances from \(P\) to two fixed points \(A\) and \(B\) is equal to twice the distance between \(A\) and \(B\). Which of the following is the locus of point \(P\)?
- Do not add choices here.
A) The line segment from A to B
B) The line passing through A and B
C) The perpendicular bisector of the line segment from A to B
D) An ellipse with A and B as foci and major axis 2d
E) A parabola

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