
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 circle C: (x+3)²+y²=100 and point B(3,0), P is a point on the circle, and the perpendicular bisector of line segment BP intersects CP at point M. Determine the equation of the trajectory of point M.

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