
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
A coordinate system and parametric equations problem, labeled as $4-4$:
Given a conic section curve with parametric equations $\begin{cases} x=2\cos \theta \\\\ y= \sqrt {3}\sin \theta \end{cases}$ where $\theta$ is a parameter, and a fixed point $A(0, \sqrt {3})$, $F_{1}$, $F_{2}$ are the left and right foci, respectively.
(I) Find the parametric equations of the line $L$ that passes through point $F_{1}$ and is perpendicular to line $AF_{2}$.
(II) Establish a polar coordinate system with the coordinate origin as the pole and the positive $x$-axis as the polar axis. Find the polar equation of line $AF_{2}$.

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