
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 $l$: 
$$
\begin{cases}
x = -1 - \frac{3}{5}t \\
y = 2 + \frac{4}{5}t
\end{cases}
\text{(where $t$ is the parameter)},
$$
and using the origin as the pole and the positive $x$-axis as the polar axis to establish a polar coordinate system, the polar equation of curve $C$ is $\rho = 2\sqrt{2}\cos \left(\theta - \frac{\pi}{4}\right)$.

$(1)$ Find the standard equation of line $l$ and the Cartesian equation of curve $C$;
$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the length of $|AB|$.

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