
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]


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Given in the Cartesian coordinate system $xOy$, the parametric equation of curve $C$ is $\begin{cases} x=3+5\cos \alpha \\ y=4+5\sin \alpha \end{cases}$, ($\alpha$ is the parameter), points $A$ and $B$ are on curve $C$. With the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar coordinates of points $A$ and $B$ are respectively $A(\rho_{1}, \frac{\pi}{6})$, $B(\rho_{2}, \frac{\pi}{2})$  
(Ⅰ) Find the polar equation of curve $C$;  
(Ⅱ) Suppose the center of curve $C$ is $M$, find the area of $\triangle MAB$.

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