
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 $C_{1}$: $\begin{cases} x=-4+ \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t\end{cases}$ (where $t$ is a parameter), $C_{2}$: $\begin{cases} x=-2+\cos \theta \\ y=1+\sin \theta\end{cases}$ (where $\theta$ is a parameter).

$(1)$ Convert the equations of $C_{1}$ and $C_{2}$ into standard form and explain what curves they represent respectively;  
$(2)$ If the curves $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$, find $|AB|$

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