
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 two points $M(-2,0)$, $N(2,0)$, and a moving point $P(x,y)$ in the coordinate plane satisfying $| \overrightarrow{MN}|\cdot | \overrightarrow{MP}|+ \overrightarrow{MN}\cdot \overrightarrow{NP}=0$, find the equation of the trajectory of the moving point $P(x,y)$.

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