
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 $xOy$, curve $C_1$ is given by $x+y=4$, and curve $C_2$ is parameterized by $\begin{cases} x=1+\cos \theta \\ y=\sin \theta \end{cases}$ with $\theta$ as the parameter. Establish a polar coordinate system with origin $O$ as the pole and the positive half-axis of $x$ as the polar axis.
$(I)$ Find the polar equations of curves $C_1$ and $C_2$.
$(II)$ Suppose the ray $\theta=\alpha$ ($\rho \geqslant 0$) intersects curves $C_1$ and $C_2$ at points $A$ and $B$, respectively. Find the maximum value of $\dfrac {|OB|}{|OA|}$.

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