
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 the parametric equations of curve $C\_1$ as $ \begin{cases} x=2\cos θ \\\\ y= \sqrt {3}\sin θ\end{cases}$ (where $θ$ is the parameter), and establishing a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C\_2$ is $ρ\cos θ-ρ\sin θ+1=0$.
1. Write the Cartesian equations for curves $C\_1$ and $C\_2$, respectively.
2. If curves $C\_1$ and $C\_2$ intersect at points $A$ and $B$, find the length of segment $AB$.

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