
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 $A$: $(x+3)^{2}+y^{2}=100$, and a fixed point $B(3,0)$ inside circle $A$. If circle $P$ passes through point $B$ and is tangent to circle $A$ internally, then the equation of the locus of the center of circle $P$ is __________.

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