
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), $C_{2}$: $\begin{cases} x=4\cos \theta \\ y=3\sin \theta \end{cases}$ ($\theta$ is the parameter).
- (I) Convert the equations of $C_{1}$ and $C_{2}$ into standard form and explain what curves they represent.
- (II) A line $l$ passing through the left vertex of curve $C_{2}$ with 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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