
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 plane rectangular coordinate system $xOy$, the parametric equations of curve $C_{1}$ are $\left\{\begin{array}{l}x=3+rcosβ,\\ y=3+rsinβ\end{array}\right.$ ($\beta$ is the parameter, $r \gt 0$), with the coordinate origin as the pole and the positive x-axis as the polar axis. The polar coordinate equation of curve $C_{2}$ is $ρ=2\sqrt{2}sin(θ+\frac{π}{4})$.  
$(1)$ If curve $C_{1}$ and $C_{2}$ have exactly one common point, find the value of $r$;  
$(2)$ If curve $C_{1}$ intersects curve $C_{2}$ at points $A$ and $B$, and $|AB|=\frac{\sqrt{30}}{2}$, find the polar coordinate equation of the line $AB$.

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