
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 the parametric equations $\begin{cases} x=\cos \alpha \ y=\sin ^{2}\alpha \end{cases}$ where $\alpha$ is a parameter. In the polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis, the curves $C\_2$ and $C\_3$ are given by the equations $\rho\cos (θ- \dfrac {π}{4})=- \dfrac { \sqrt {2}}{2}$ and $\rho=2\sin θ$, respectively.

1. Find the rectangular coordinates of the intersection point(s) of the curves $C\_1$ and $C\_2$.
2. Let $A$ and $B$ be moving points on the curves $C\_2$ and $C\_3$, respectively. Find the maximum value of $|AB|$.

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