
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 line $l$: $\begin{cases} x=2+t \\ y=-1-t \end{cases}$ ($t$ is the parameter) and the curve $C$ with polar coordinate equation $p=3$.
(I) Let $A$ and $B$ be the intersection points of line $l$ and curve $C$. Find the length of segment $|AB|$.
(II) If $P$ is any point on curve $C$, find the maximum area of $\triangle ABP$.

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