
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 curve $C$: $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$, and the line $l$: $\begin{cases} x=2+t \\ y=2-2t \end{cases}$ ($t$ is a parameter)
(I) Write the parametric equation of the curve $C$ and the general equation of the line $l$.
(II) Through any point $P$ on the curve $C$, draw a line that forms a $30^\circ$ angle with $l$, intersecting $l$ at point $A$. Find the maximum and minimum values of $|PA|$.

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