
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 $C_1: (x-4)^2+y^2=169$ and $C_2: (x+4)^2+y^2=9$, find the equation of the trajectory of the center $M$ of a circle that is inside $C_1$ and tangent to $C_1$ internally, and tangent to $C_2$ externally.

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