
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is: $$\begin{cases} x=- \sqrt {6}- \sqrt {2}t \\ y=2 \sqrt {6}+ \sqrt {2}t\end{cases}$$ (where $t$ is the parameter). In the polar coordinate system (with the same unit length as the Cartesian coordinate system $xOy$, and with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis), the equation of circle $C$ is $$ρ=4 \sqrt {6}cosθ$$.
(1) Find the rectangular coordinate equation of circle $C$;
(2) Suppose circle $C$ intersects line $l$ at points $A$ and $B$, find the length of $|AB|$.

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