
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 points M(0, -2) and N(0, 2), and a moving point P(x, y) that satisfies the equation $$\sqrt {x^{2}+y^{2}+4y+4}+ \sqrt {x^{2}+y^{2}-4y+4}=10$$, if |PM| = 7, then find |PN|.

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