
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 $(xOy)$, curve $C\_1$: $\begin{cases} x=r\cos \theta \ y=r\sin \theta \end{cases}$ ($\theta$ is the 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 the parameter), establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of $x$ as the polar axis. The ray $\theta=\alpha(0 < \alpha < \frac {\pi}{2})$ intersects curve $C\_1$ at point $N$ and curve $C\_2$ at points $O$ and $P$, with the maximum value of $|PN|$ being $2 \sqrt {2}$.

1. Convert curves $C\_1$ and $C\_2$ into polar coordinate equations and find the value of $r$.
2. The ray $\theta=\alpha+ \frac {\pi}{4}$ intersects curve $C\_1$ at point $Q$ and curve $C\_2$ at points $O$ and $M$. Find the maximum value of the area of quadrilateral $MPNQ$.

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