
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 $C$: 
$$
\begin{cases}
x= \sqrt{2}\cos \theta \\
y=\sin \theta
\end{cases} (\theta \text{ is the parameter})
$$
and a fixed point $A\left(0, \frac{ \sqrt{3}}{3}\right)$, with $F_{1}$ and $F_{2}$ being the left and right foci of the conic curve $C$ respectively.  
(Ⅰ) Find the parametric equation of the line $l$ that passes through point $F_{2}$ and is perpendicular to the line $AF_{1}$.  
(Ⅱ) Under the condition of (Ⅰ), the line $l$ intersects the curve $C$ at points $M$ and $N$, find $|MN|$.

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