
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 $⊙C_{1}$: $x^{2}+(y+1)^{2}=25$ and $⊙C_{2}$: $x^{2}+(y-2)^{2}=1$, find the trajectory equation of the moving circle's center $M$ that is internally tangent to $⊙C_{1}$ and externally tangent to $⊙C_{2}$.

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