
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 $A:(x+4)^2+y^2=25$ and $B:(x-4)^2+y^2=1$, a moving circle $M$ is externally tangent to both fixed circles. Let the locus of the center of moving circle $M$ be curve $C$.

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

(II) If line $l$ intersects curve $C$ at points $P$ and $Q$, and $OP \perp OQ$. Is $\frac{1}{|OP|^2}+\frac{1}{|OQ|^2}$ a constant value? If it is, find the value; if not, explain the reason.

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