
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 circles, ⊙M: $(x+1)^2+y^2=1$ and ⊙N: $(x-1)^2+y^2=9$, there is a moving circle P that is externally tangent to ⊙M and internally tangent to ⊙N. The trajectory of the center of circle P is curve C.  
(1) Find the equation of C;  
(2) Let l be a line that is tangent to both ⊙P and ⊙M. When the radius of ⊙P is at its maximum, find the equation of line l.

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