
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
Suppose curve $C: \frac{{x}^{2}}{4}+ \frac{{y}^{2}}{9}=1$, and line $l:\begin{cases}x=2+t \
y=2-2t\end{cases} (t \text{ is a parameter})$.

(1) Write the parametric equation of curve $C$ and the general equation of line $l$;

(2) Draw a line through an arbitrary point $P$ on curve $C$, such that the angle between the line and $l$ is $30^{\circ}$, intersecting $l$ at point $A$. Calculate the maximum and minimum values of $|PA|$.

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