
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
Given that the pole of the polar coordinate system is located at the origin $O$ of the rectangular coordinate system, the polar axis coincides with the positive semi-axis of the $x$-axis, and the unit of length is the same. The equation of the curve $C\_1$ is given by $\begin{cases} x=\sqrt{2}\cos\theta \ y=\sin\theta \end{cases}\ (\theta\text{ is a parameter})$, and the polar coordinate equation of the curve $C\_2$ is given by $C\_2:\rho\cos\theta+\rho\sin\theta=1$. The curves $C\_1$ and $C\_2$ intersect at points $A$ and $B$.

1. Find the rectangular coordinate equations of the curves $C\_1$ and $C\_2$.
2. Find the value of $|AB|$.
3. Find the product of the distances from the point $M(-1, 2)$ to the points $A$ and $B$.

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