
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 that the ratio of the distance from moving point M to fixed point F ($-\sqrt {3}$, $0$) to its distance from line m: $x=-\frac{4\sqrt{3}}{3}$ is a constant $\frac{\sqrt{3}}{2}$, denote the trajectory of moving point M as curve C.
(I) Find the equation of curve C.
(II) If line l₁: $y=kx+t_1$ intersects curve C at two distinct points A and B, and line l₂: $y=kx+t_2$ ($t_1 \neq t_2$) intersects curve C at two distinct points D and E, and $|AB|=|DE|$, find the maximum area S of the convex quadrilateral with vertices A, B, D, and E.

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