
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 $(xOy)$, the parametric equations of curve $C\_1$ are given by $\begin{cases} x=1-\frac{\sqrt{2}}{2}t \ y=3+\frac{\sqrt{2}}{2}t \end{cases} (t \text{ is the parameter})$, and the parametric equations of curve $C\_2$ are given by $\begin{cases} x=1+\cos \varphi \ y=\sin \varphi \end{cases} (\phi \text{ is the parameter})$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.

(1) Find the polar equations of curves $C\_1$ and $C\_2$;

(2) If ray $l:θ=α ( ρ > 0 )$ intersects $C\_1$ and $C\_2$ at points $A$ and $B$ respectively, find the maximum value of $\frac{|OB|}{|OA|}$.

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