
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 $M(-2,0)$ and $N(2,0)$, and point $P$ as a moving point on the coordinate plane that satisfies the condition $| \overrightarrow{MN}| \cdot | \overrightarrow{MP}| + \overrightarrow{MN} \cdot \overrightarrow{NP} = 0$, determine the trajectory equation of the moving point $P(x,y)$.

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