
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 the conic curve $$\begin{cases} \left.\begin{matrix}x=3\cos\theta \\ y=2\sqrt{2}\sin\theta\end{matrix}\right.\end{cases}(\theta \text{ is a parameter})$$ and a fixed point $$A\left(0, \frac{\sqrt{3}}{3}\right)$$, $F_1$ and $F_2$ are the left and right foci of the conic curve respectively.  
(1) Find the parametric equation of the line $l$ that passes through point $F_2$ and is perpendicular to the line $AF_1$.  
(2) With the origin as the pole and the positive half-axis of the x-axis as the polar axis, establish a polar coordinate system and find the polar equation of the line $AF_2$.

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