
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 
$$
\begin{cases} 
x = \frac{\sqrt{3}}{2}t \\
y = 1 + \frac{1}{2}t
\end{cases}
(t \text{ is the parameter}).
$$
(Ⅰ) Find the Cartesian coordinate equation of curve $C$ and the general equation of line $l$;  
(Ⅱ) Assume curve $C$ and line $l$ intersect at points $A$ and $B$, and point $P$ is another point on curve $C$ distinct from $A$ and $B$. Calculate the maximum area of $\triangle PAB$.

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