
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 rectangular coordinate system $(xoy)$, the curve $C_1: \begin{cases} x=1+\cos \alpha \\ y=\sin ^{2}\alpha - \frac {9}{4} \end{cases}(\alpha$ is the parameter, $\alpha \in R$), and in the polar coordinate system with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis (taking the same unit of length), the curve $C_2: \rho \sin (\theta + \frac {\pi}{4})=-\frac {\sqrt {2}}{2}$, and the curve $C_3: \rho = 2\cos \theta$.
(I) Find the rectangular coordinates of the intersection point $M$ of the curves $C_1$ and $C_2$;
(II) Suppose $A$ and $B$ are moving points on the curves $C_2$ and $C_3$, respectively. Find the minimum value of $|AB|$.

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