
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 $C$: $\begin{cases} x=3\cos \theta \\ y=2\sin \theta \end{cases}(\theta \text{ is a parameter})$ and the line $l$: $\begin{cases} x=2+t \\ y=2-2t \end{cases}(t \text{ is a parameter})$.
(1) Write the general equations for the curve $C$ and the line $l$;
(2) Through any point $P$ on the curve $C$, draw a line that forms a $45^{\circ}$ 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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