
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 $xoy$, the parametric equation of curve $C_1$ is $$\begin{cases} x=1+\cos\beta \\ y=\sin\beta \end{cases}$$ (where $\beta$ is the parameter). With the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established, and the polar equation of curve $C_2$ is $\rho=4\cos\theta$.
(Ⅰ) Convert the equation of curve $C_1$ into a polar equation;
(Ⅱ) Given that the parametric equation of line $l$ is $$\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$$ ($$\frac{\pi}{2}<\alpha<\pi$$, $t$ is the parameter, $t\neq0$), $l$ intersects $C_1$ at point $A$, and $l$ intersects $C_2$ at point $B$, and $|AB|=\sqrt{3}$, find the value of $\alpha$.

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