
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 $(xOy)$, the parametric equations of curve $C\_1$ are given by $\begin{cases} x=1+\cos α \ y=\sin α\end{cases}(α$ is the parameter$)$; in the polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of curve $C\_2$ is given by $ρ\cos ^2θ=2\sin θ$;
(1) Find the polar equation of curve $C\_1$ and the Cartesian equation of curve $C\_2$;
(2) If ray $l$: $y=kx(x\geqslant 0)$ intersects curves $C\_1$, $C\_2$ at points $A$, $B$ (where $A$, $B$ differ from the origin), find the range of $|OA|⋅|OB|$ when $k∈[1, \sqrt {3})$.

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