
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 $C\_1$ is given by: $\begin{cases} x=\cos \alpha, \ y=\sin ^{2}\alpha \end{cases} (\alpha$ is the parameter$)$, and in the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the curves $C\_2$ and $C\_3$ are given by: $C\_2$: $\rho\cos \left( \theta- \dfrac{\pi}{4} \right)=- \dfrac{ \sqrt{2}}{2}$ and $C\_3$: $\rho=2\sin \theta$.

(1) Find the rectangular 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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