
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 point M in the Cartesian coordinate system, the ratio of the distances from M to two fixed points M<sub>1</sub> (26, 1) and M<sub>2</sub> (2, 1) is equal to 5.  
(Ⅰ) Find the equation of the trajectory of point M and describe what shape the trajectory is;  
(Ⅱ) Let the trajectory of point M be C. A line l passing through point P (-2, 3) intersects C, and the length of the chord is 8. Find the equation of line l.

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