
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 parameter equation of line $l$ is given by $\begin{cases}x=1+\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \end{cases}$ $(t)$ is a parameter, and the parameter equation of ellipse $C$ is given by $\begin{cases}x=\cos \theta \\ y=2\sin \theta \end{cases}$ $(\theta)$ is a parameter. Suppose line $l$ intersects ellipse $C$ at points $A$ and $B$, find the length of segment $AB$.

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