
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 $F_1$: $(x+1)^2+y^2=1$, and circle $F_2$: $(x-1)^2+y^2=25$, if a moving circle $C$ is externally tangent to circle $F_1$ and internally tangent to circle $F_2$, find the equation of the trajectory of the center $C$ of the moving circle.

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