
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, $0<r<4$), 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), establishing a polar coordinate system with the origin as the pole and the non-negative half-axis of x as the polar axis, the ray $\theta=\alpha$ ($0<\alpha<\frac{\pi}{2}$) intersects curve $C_1$ at point N, and intersects curve $C_2$ at points O and P, and the maximum value of $|PN|$ is $2\sqrt{2}$.
(1) Convert curves $C_1$ and $C_2$ into polar equations, and find the value of $r$;
(2) The ray $\theta=\alpha+ \frac{\pi}{4}$ intersects curve $C_1$ at point Q, and intersects 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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