
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
A coordinate system and parametric equations are given in the problem 4-4 of the elective course.

Given the curve $C: \frac{x^2}{4} + \frac{y^2}{9} = 1$, and the line $l$ defined by the parametric equations: $\begin{cases} x = 2 + t \\ y = 2 - 2t \end{cases}$ (where $t$ is a parameter).

(1) Write the parametric equations for the curve $C$ and the general equation for the line $l$.

(2) A line passing through any point $P$ on the curve $C$ intersects $l$ at point $A$ forming an angle of $30^{\circ}$ with $l$. Find the maximum and minimum values of $|PA|$.

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