
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 the fixed point $F_1(-n,0)$, the locus of point $P$ is sought, where a moving circle $M$ with diameter $PF_1$ is tangent internally to a fixed circle $C$: $x^2+y^2=m^2 ~(m > n > 0)$. Find the equation of the locus.

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