
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 $\begin{cases} & x=-1-\dfrac{3}{5}t \\ & y=2+\dfrac{4}{5}t \end{cases}$ (where $t$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, establishing a polar coordinate system, the polar equation of curve $C$ is $\rho=2 \sqrt{2}\cos \left(\theta- \dfrac{\pi}{4}\right)$.

$(1)$ Find the general equation of line $l$ and the Cartesian coordinate equation of curve $C$;

$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find $|AB|$.

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