
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(x, y) in the Cartesian coordinate system, with points A(-4, 0), B(-1, 0), and in triangle $\triangle ABM$, $|MA| = 2|MB|$.  
(Ⅰ) Find the equation of the trajectory C of point M and the range of the perimeter of $\triangle ABM$;  
(Ⅱ) The line MB intersects the trajectory C at another point M', find the range of $$\frac {S_{\triangle AMB}}{S_{\triangle AM'B}}$$.

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