
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 coordinate system and parametric equations section of the Optional 4-4 topic, it's given that the conic curve is defined by the parametric equations $\begin{cases} x=2\cos\theta \\ y= \sqrt{3}\sin\theta\end{cases}$ (with $\theta$ as the parameter) and the fixed point A (0, $\sqrt{3}$). Let $F_1$ and $F_2$ be the left and right focal points, respectively.
(Ⅰ) Find the parametric equation of the line $L$ that passes through point $F_1$ and is perpendicular to line $AF_2$.
(Ⅱ) With the coordinate origin as the pole and the positive x-axis as the polar axis, establish a polar coordinate system and find the polar equation of line $AF_2$.

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