
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 $C: \frac{4x^{2}}{9}+ \frac{y^{2}}{16}=1$ and the line $l: \begin{cases} x=3+t \\ y=5-2t \end{cases} (t \text{ is the parameter})$.
(I) Write the parametric equation of the curve $C$ and the general equation of the line $l$;
(II) Draw a line through any point $P$ on the curve $C$ such that it 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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