
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 Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\begin{cases} x=1+\cos \phi \\ y=\sin \phi \end{cases}$, where $\phi$ is the parameter. The equation of curve $C_{2}$ is $\dfrac {x^{2}}{8}+ \dfrac {y^{2}}{4}=1$. Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis.  
$(1)$ Find the polar equations of curves $C_{1}$ and $C_{2}$.  
$(2)$ The ray $l: \theta=\alpha (\rho \geqslant 0)$ intersects curves $C_{1}$ and $C_{2}$ at points $A$ and $B$ respectively, and both $A$ and $B$ are different from the origin $O$. When $0 < \alpha < \dfrac {\pi}{2}$, find the minimum value of $|OB|^{2}-|OA|^{2}$.

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