
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
In the polar coordinate system, the ray $l:θ= \frac{π}{6}$ intersects the circle $C:ρ=2$ at point $A$, and the equation of the ellipse $D$ is ${ρ}^{2}= \frac{3}{1+2{\sin }^{2}θ}$. Establish a rectangular coordinate system $xOy$ with the pole as the origin and the positive semi-axis of the polar axis as the major axis of the ellipse.

(1) Find the rectangular coordinates of point $A$ and the parametric equation of the ellipse $D$;

(2) If $E$ is the lower vertex of the ellipse $D$, and $F$ is any point on the ellipse $D$, find the range of values for $\overset{→}{AE}· \overset{→}{AF}$.

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