
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 $C_1: \begin{cases} & x=-2+\cos t \\ & y=1+\sin t \end{cases}$ (where $t$ is a parameter), and $C_2: \begin{cases} & x=4\cos \theta \\ & y=3\sin \theta \end{cases}$ (where $\theta$ is a parameter).

(I) Convert the equations of $C_1$ and $C_2$ into standard form and explain what curves they represent;

(II) A line $l$ that passes through the left vertex of curve $C_2$ and has a slope angle of $\frac{\pi}{4}$ intersects curve $C_1$ at points $A$ and $B$. Find $|AB|$.

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