
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 M:(x+√7)^2 + y^2 = 64, fixed point N(√7, 0), point P is a moving point on circle M, point Q is on NP, and point G is on line segment MP, satisfying NP = 2NQ and GQ ⋅ NP = 0. Determine the trajectory equation of point G.

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