
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 point F(1, 0), and the moving point M's distance to line l: x = 4 is d. The ratio of $|MF|$ to $d$ is $\frac{1}{2}$. Let the trajectory of the moving point M be curve E.

1. Find the equation of curve E.
2. Draw two perpendicular lines through point F that intersect curve E at points A, B and C, D, respectively. Find the minimum area of quadrilateral ABCD.

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