
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 Cartesian coordinate system $(xOy)$, the parametric equations of the curve $C$ are $\begin{cases} x=3+5\cos \alpha \\ y=4+5\sin \alpha \end{cases}$ (where $\alpha$ is the parameter). Points $A$ and $B$ lie on the curve $C$. Using the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar coordinates of points $A$ and $B$ are $A(\rho\_1, \frac{\pi}{6})$ and $B(\rho\_2, \theta)$, respectively, where $\theta \in [0, \pi]$.

(1) Find the polar equation of the curve $C$.

(2) Let $M$ be the center of the curve $C$. Find the maximum area of $\triangle MAB$ and the polar coordinates of point $B$ in this case.

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