
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 line $l$: $3x-4y+m=0$ passes through the point $(-1,2)$, in the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the equation of curve $G$ is $\rho=2 \sqrt {2}\sin (\theta+ \dfrac {\pi}{4})$. The square $OABC$ is inscribed in curve $G$, and $O$, $A$, $B$, $C$ are arranged counterclockwise, with $A$ on the polar axis.  
(Ⅰ) Write the parametric equation of line $l$ and the Cartesian coordinate equation of curve $G$;  
(Ⅱ) If point $P$ is any point on line $l$, find the minimum value of $PO^{2}+PA^{2}+PB^{2}+PC^{2}$.

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