
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 that the moving point $M(x,y)$ and two fixed points $P(26,1)$, $Q(2,1)$ on the coordinate plane, and $|MP|=5|MQ|$.

(I) Find the trajectory equation of point $M$ and explain what kind of graph it is.

(II) Denote the trajectory in (I) as $C$, and the length of the line segment intercepted by line $l$ passing through point $N(-2,3)$ on $C$ is $8$. Find the equation of line $l$.

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