
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 $C$: $\begin{cases}x=3\cos \theta, \ y=2\sin \theta\end{cases}$ ($\theta$ is a parameter) and the line $l$: $\begin{cases}x=2+t, \ y=2-2t\end{cases}$ ($t$ is a parameter).

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

(2) Draw a line through any point $P$ on curve $C$ such that it 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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