
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} $ ($t$ is the parameter), and $C\_2$: $ \begin{cases} x=4 \cos \theta \\ y=3 \sin \theta \end{cases} $ ($\theta$ is the parameter).

(I) Convert the equations of $C\_1$ and $C\_2$ into general form and describe the type of curve each represents.
(II) A line $l$ passes through the left vertex of curve $C\_2$ with a slope angle of $\frac{\pi }{4}$. It intersects with curve $C\_1$ at points $A$ and $B$. Calculate $|AB|$.

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