
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
A coordinate system and parametric equations (4-4): In the rectangular coordinate system $xOy$, curve $C\_1$: $\begin{cases} & x=r\cos \theta \\ & y=r\sin \theta \\ \end{cases} (\theta$ is a parameter, $0 < r < 4$), and curve $C\_2$: $\begin{cases} & x=2+2\sqrt{2}\cos \theta \\ & y=2+2\sqrt{2}\sin \theta \\ \end{cases} (\theta$ is a parameter), the origin is the pole, and the non-negative semi-axis of the $x$-axis is the polar axis to establish a polar coordinate system. Ray $\theta=\alpha (0 < \alpha < \frac{\pi }{2})$ intersects curve $C\_1$ at point $N$ and curve $C\_2$ at points $O$, $P$, such that $|PN|$ has a maximum value of $2\sqrt{2}$.

(1) Convert curves $C\_1$ and $C\_2$ into polar coordinate equations and find the value of $r$;

(2) Ray $\theta =\alpha +\frac{\pi }{4}$ intersects curve $C\_1$ at point $Q$ and curve $C\_2$ at points $O$, $M$. Find the maximum value of the area of quadrilateral $MPNQ$.

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