
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 polar equation of curve $C$ is $\rho=4\sin \theta$, and the parametric equation of line $l$ is $\begin{cases} & x=\dfrac{\sqrt{3}}{2}t \\ & y=1+\dfrac{1}{2}t \end{cases}$ (where $t$ is the parameter),

(Ⅰ) Find the rectangular coordinate equation of curve $C$ and the general equation of line $l$:

(Ⅱ) Suppose curve $C$ and line $l$ intersect at points $A$ and $B$, and point $P$ is another point on curve $C$ different from $A$ and $B$. Find the maximum area of $\triangle PAB$.

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