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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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system
In the Cartesian coordinate system \(xOy\), the parametric equation of curve \(C_1\) is 
\[
\begin{cases}
x=1+\cos \beta \\
y=\sin \beta
\end{cases} (\beta \text{ is the parameter}),
\]
with the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve \(C_2\) is 
\[
\rho=4\cos \theta.
\]
(1) Convert the equation of \(C_1\) to a standard equation and the equation of \(C_2\) to a Cartesian coordinate equation.
(2) Given that the parametric equation of line \(l\) is 
\[
\begin{cases}
x=t\cos \alpha \\
y=t\sin \alpha 
\end{cases} \left( \frac {\pi}{2} < \alpha < \pi, t \text{ is the parameter and } t\neq 0 \right),
\]
line \(l\) intersects \(C_1\) at point \(A\) and \(C_2\) 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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