
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 A: $(x+2)^2+y^2=1$, and circle B: $(x-2)^2+y^2=49$, a moving circle P is tangent to both circle A and circle B.  
(1) Find the equation of the trajectory of the center of circle P;  
(2) Given point N $(2, \frac{5}{3})$, draw ray AN, which intersects the "trajectory of point P" at another point M, find the perimeter of $\triangle MNB$.

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