
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 that the pole of the polar coordinate system is the origin of the rectangular coordinate system, and the polar axis is the positive semi-axis of the $x$-axis $(x)$, the polar coordinate equation of the curve $C$ is $ρ=8\sin θ$.
$(1)$ Find the rectangular coordinate equation of the curve $C$;
$(2)$ Given that the line $\begin{cases} x=t \\ y=t+2 \end{cases} (t \text{ is the parameter})$ intersects the 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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