
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 parametric equation of line $l$ as
$$
\begin{cases}
x = t\cos \alpha \\
y = -1 + t\sin \alpha
\end{cases}
(t \text{ is a parameter}),
$$
in a polar coordinate system with the origin $O$ as the pole and the non-negative half of the x-axis as the polar axis, the polar equation of curve $C$ is $\rho = 6\sin \theta$.

(1) Write the rectangular coordinate equation of curve $C$;

(2) Given $P(0,-1)$, if line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $\overrightarrow{PA} \cdot \overrightarrow{PB}$.

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