
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+ \sqrt {10}\cos θ \\ y= \sqrt {10}\sin θ\\end{cases} (θ$ is the parameter), and the polar equation of curve $C\_2$ as $ρ=2\cos θ+6\sin θ$.

1. Convert the parametric equations of curve $C\_1$ into a standard form and convert the polar equation of curve $C\_2$ into rectangular coordinates.
2. Determine if curves $C\_1$ and $C\_2$ intersect. If they intersect, find the length of the common chord. If they do not intersect, explain why.

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