
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 line $x+y-2 \sqrt {2}=0$ passing through the focus of the ellipse $(M)$: $\frac{x^{2}}{b^{2}}+ \frac{y^{2}}{a^{2}}=1 (a > b > 0)$ intersects $(M)$ at points $P$ and $Q$. $G$ is the midpoint of $PQ$, and the slope of $OG$ is $9$.
(I) Find the equation of $(M)$;
(II) $A$ and $B$ are the left and right vertices of $(M)$, and $C$ and $D$ are two points on $(M)$. If $AC \perp BD$, find the maximum value of the area of the quadrilateral $ABCD$.

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