
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 $$C_{1}: \begin{cases} x=1+\cos\alpha \\ y=\sin^{2}\alpha - \frac {9}{4} \end{cases}$$ (where $\alpha$ is a parameter, $\alpha \in \mathbb{R}$), is given. In the polar coordinate system with the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis (using 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 Cartesian coordinates of the intersection point $M$ of curve $C_{1}$ and $C_{2}$;  
(Ⅱ) Let $A$ and $B$ be 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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