
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 rectangular coordinate system $(xOy)$, with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system. The polar coordinate equation of the curve $C$ is $ρ=4\sin θ$.
$(1)$ Find the rectangular coordinate equation of the curve $C$;
$(2)$ If the curve $C_{1}$: $ \begin{cases} x=3+r\cos α \\ y=-2+r\sin α \end{cases}(α$ is a parameter$)$ and the curve $C$ are tangent to each other, find the value of $r$.

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