
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 $$C_{1}: \begin{cases} x = \cos\alpha \\ y = \sin^{2}\alpha \end{cases}$$ (where $\alpha$ is a parameter) is given. In the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the curve $$C_{2}: \rho\cos(\theta - \frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$$ and the curve $C_{3}: \rho = 2\sin\theta$ are also given.  
(1) Find the Cartesian coordinates of the intersection point $M$ of curve $C_{1}$ 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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