
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 $(xOy)$, it is known that curve $C\_1$: $x+y=1$ and curve $C\_2$: $\begin{cases} x=2+2\cos\phi \ y=2\sin\phi \end{cases} (\phi \in [0,2\pi))$ with the coordinate origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis to establish a polar coordinate system.
(I) Write the polar coordinate equations of curves $C\_1$ and $C\_2$;
(II) In the polar coordinate system, point $A$ is the common point of ray $l$: $\theta=\alpha (\rho\geqslant 0)$ and $C\_1$, and point $B$ is the common point of $l$ and $C\_2$. When $\alpha$ varies in the interval $[0, \dfrac{\pi}{2}]$, find the maximum value of $\dfrac{|OB|}{|OA|}$.

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