
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
The polar coordinate equation of circle $C$ is $ρ=2 \sqrt{2}\cos \left(θ+ \dfrac{3}{4}π\right)$, and the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system. The polar axis coincides with the non-negative half of the $x$-axis, and the length units are the same. The parametric equations of line $l$ are $\begin{cases}x=-1- \dfrac{ \sqrt{2}}{2}t \\ y= \dfrac{ \sqrt{2}}{2}t\end{cases} (t \text{ is the parameter})$.

(1) Find the rectangular coordinate equation of $C$ and the polar coordinates of its center.
(2) Lines $l$ and $C$ intersect at points $A$ and $B$. Find $|AB|$.

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