
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
A coordinate system and parametric equations problem (4-4):

In the rectangular coordinate system $xoy$, a curve $C_1$ is defined by the parametric equations $\begin{cases} x = 1 + \cos \alpha \\ y = \sin^2 \alpha - \frac{9}{4} \end{cases}$, where $\alpha$ is the parameter and $\alpha \in \mathbb{R}$. In the polar coordinate system with the origin $O$ as the pole and the nonnegative $x$-axis as the polar axis (using the same length units), there are two other curves: $C_2: \rho \sin \left( \theta + \frac{\pi}{4} \right) = -\frac{\sqrt{2}}{2}$ and $C_3: \rho = 2 \cos \theta$.

(I) Find the rectangular coordinates of the intersection point $M$ of the curves $C_1$ and $C_2$.
(II) Let $A$ and $B$ be moving points on the curves $C_2$ and $C_3$, respectively. Find the minimum value of the distance $|AB|$.

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