
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 a moving circle $M$ that is externally tangent to circle $C_{1}$: $(x+5)^{2}+y^{2}=16$ and internally tangent to circle $C_{2}$: $(x-5)^{2}+y^{2}=16$, determine the trajectory equation of the moving circle's center.

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