
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 a curve C in the Cartesian coordinate system xOy, whose parametric equations are:
$$
\begin{cases}
x = 3 + 5\cos\alpha \\
y = 4 + 5\sin\alpha
\end{cases},
$$
where α is the parameter. Points A and B lie on curve C. Taking 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(ρ₁, $\frac{\pi}{6}$) and B(ρ₂, $\frac{\pi}{2}$) respectively.
(Ⅰ) Find the polar equation of curve C.
(Ⅱ) Suppose the center of curve C is M, determine the area of triangle MAB.

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