
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 $xOy$, given the parametric equation of line $l$ as $$\begin{cases} x=1+t, \\ y=t, \end{cases}$$ where $t$ is the parameter, and the parametric equation of ellipse $C$ as $$\begin{cases} x= \sqrt {2}\cos{\theta}, \\ y=\sin{\theta}, \end{cases}$$ where $\theta$ is the parameter. Let line $l$ intersect ellipse $C$ at points $A$ and $B$. Find the length of segment $AB$.

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