
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
Given the parametric equations of curve $C\_1$ are $x=2\cos \phi$ and $y=2\sin \phi$, where $\phi$ is the parameter. Establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C\_2$ is $\rho= \frac {6}{ \sqrt {4+5\sin ^{2}\theta}}$. The vertices of square $ABCD$ are all on $C\_1$, and $A$, $B$, $C$, $D$ are arranged in counterclockwise order, with the polar coordinates of point $A$ being $(2, \frac {\pi}{6})$.
(I) Find the rectangular coordinates of points $A$, $B$, $C$, and $D$.
(II) Let $P$ be any point on $C\_2$, find the maximum value of $|PA|^{2}+|PB|^{2}+|PC|^{2}+|PD|^{2}$.

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