
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) is half the distance from point E(1, 0) to point F(4, 0).  
(I) Find the equation of the trajectory of point M;  
(II) Given points A, C, B, D are four points on the trajectory of point M, and AC, BD are perpendicular to each other with the foot of the perpendicular being M(1, 1), find the range of the area of quadrilateral ABCD.

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