
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 curves $C\_1$: $\begin{cases} x=-2+\cos t\\y=1+\sin t\end{cases} (t$ as a parameter $)$, and $C\_2$: $\begin{cases} x=-4+ \frac { \sqrt {2}}{2}s \\y= \frac { \sqrt {2}}{2}s\end{cases} (s$ as a parameter $)$.
(1) Convert the equations of $C\_1$ and $C\_2$ into ordinary equations and explain what kind of curves they represent.
(2) Curve $C\_2$ intersects curve $C\_1$ at points $A$ and $B$. Calculate $|AB|$.

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