
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
In the cartesian coordinate system $(xOy)$, the parametric equations of the curve $C$ are given by $C: \begin{cases} x=3 \cos \alpha \\ y=\sin \alpha \end{cases} \; (\alpha \text{ is the parameter})$, and the parametric equations of the line $l$ are given by $\begin{cases} x=-t+2 \\ y=t \end{cases} \; (t \text{ is the parameter})$.

(1) Find the cartesian equations of the curve $C$ and the line $l$.

(2) If the line $l$ intersects the curve $C$ at points $A$ and $B$, find the length of the line segment $\left| AB \right|$.

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