
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 the curves $C\_1$ and $C\_2$ are $\begin{cases}x=4t^2 \\\\ y=4t\end{cases} (t \text{ is the parameter})$ and $\begin{cases}x=\cos \phi \\\\ y=1+\sin \phi\end{cases} (\phi \text{ is the parameter})$, respectively. Establish a coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.
(I) Find the Cartesian equation of curve $C\_1$ and the polar equation of curve $C\_2$;
(II) The ray $OM:θ=α\left(α∈\left[\frac{π}{6}, \frac{π}{4}\right]\right)$ intersects curve $C\_1$ at points $O$ and $P$, and 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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