
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 $(xOy)$, curve $C\_1$: $x+y=4$, curve $C\_2$: $\begin{cases} x=1+\cos θ \ y=\sin θ\end{cases}(θ)$ as the parameter, with the coordinate origin $O$ as the pole, the positive semi-axis of $x$ as the polar axis to establish the polar coordinate system.
(1) Find the polar coordinate equations of curves $C\_1$ and $C\_2$;
(2) If ray $l$: $θ=α(p > 0)$ 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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