
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 parametric equations of the curve $C\_1$ are given by $ \begin{cases} x=1- \frac { \sqrt {2}}{2}t \\ y=1+ \frac { \sqrt {2}}{2}t \end{cases} (t \text{ is the parameter})$, and in the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of the curve $C\_2$ is $ρ^{2}-2ρ\cos θ-3=0$.

1. Find the cartesian equation of $C\_1$ and the polar equation of $C\_2$.
2. $C\_1$ and $C\_2$ have two common points $A$ and $B$. Find the length of the line segment $AB$.

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