
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, there are two curves: Curve C<sub>1</sub>: $\sqrt{3}x + y - 4 = 0$ and Curve C<sub>2</sub>: $\begin{cases} x = \cos\theta \\ y = 1 + \sin\theta \end{cases}$ (where $\theta$ is the parameter). With the origin O as the pole and the positive x-axis as the polar axis, a polar coordinate system is established.
(Ⅰ) Find the polar equations of C<sub>1</sub> and C<sub>2</sub>.
(Ⅱ) Curve C<sub>3</sub> is defined by $\begin{cases} x = t\cos\alpha \\ y = t\sin\alpha \end{cases}$ (where $t$ is the parameter, $t > 0$ and $0 < \alpha < \frac{\pi}{2}$) and intersects C<sub>1</sub> and C<sub>2</sub> at points A and B, respectively. What value should $\alpha$ take to maximize the value of $\frac{|OB|}{|OA|}$?

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