
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
In the rectangular coordinate system $xOy$, the parametric equation of line $l$ is $$\begin{cases} x=3- \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}$$ ($t$ is the parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho=4\sqrt {3}\sin\theta$.

1. Find the rectangular equation of curve $C$ and the general equation of line $l$.
2. Line $l$ intersects curve $C$ at points $A$ and $B$. The midpoint of chord $AB$ is $Q$, and point $P(0,3\sqrt {3})$, find $|PQ|$.

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