
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 curve $C\_1: \begin{cases} x=\cos \alpha \\ y=\sin^2 \alpha \end{cases} (\alpha$ is the parameter$)$, in the polar coordinate system with the pole $O$ and the positive half of the $x$-axis as the polar axis, the curve $C\_2: \rho \cos (\theta - \frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$, curve $C\_3$: $\rho = 2 \sin \theta$.
(1) Find the Cartesian coordinates of the intersection point $M$ of curves $C\_1$ and $C\_2$;
(2) Let points $A$ and $B$ be moving points on 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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