
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 $\begin{cases} x=2+2\cos α, \ y=2\sin α \end{cases}$ ($α$ is the parameter), and the parametric equations of curve $C\_2$ are $\begin{cases} x=2\cos β, \ y=2+2\sin β \end{cases}$ ($β$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis.

1. Find the polar equations of curves $C\_1$ and $C\_2$;
2. Given ray $l\_1$: $θ=α(0 < α < \dfrac{π}{2})$, rotate ray $l\_1$ counterclockwise by $\dfrac{π}{6}$ to obtain ray $l\_2$: $θ=α-\dfrac{π}{6}$, where ray $l\_1$ intersects curve $C\_1$ at points $O$ and $P$, and ray $l\_2$ intersects curve $C\_2$ at points $O$ and $Q$. Find the maximum value of $|OP|⋅|OQ|$.

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