
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 fixed points in the Cartesian coordinate system, A(2, 3) and B(5, 3), if the moving point M satisfies $|AM| = 2|BM|$.  
(1) Find the equation of the trajectory of point M;  
(2) If the line $l: y = x - 5$ intersects the trajectory of M at points C and D, find the length of CD.

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