
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 circles $M$: $((x+1)^{2}+y^{2}=1)$ and $N$: $((x-1)^{2}+y^{2}=25)$, a moving circle $P$ is externally tangent to circle $M$ and internally tangent to circle $N$. The locus of the center of circle $P$ forms a curve $C$.

(I) Find the equation of curve $C$;

(II) A line passing through a point $Q(1, \frac{8}{3})$ on curve $C$ intersects the curve at points $A$ and $B$. The slopes of $OA$ and $OB$ are opposite. Find the slope of line $AB$.

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