
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 plane $(xOy)$, a line $l$ passes through point $P(1, 0)$ with an angle of inclination $\frac{π}{3}$. An ellipse $C$ has the parametric equations $\begin{cases} x = \cos{\theta} \\ y = 2\sin{\theta} \end{cases} (\theta \text{ is the parameter})$.

(1) Find the parametric equation of line $l$ and the cartesian equation of ellipse $C$.
(2) If 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}
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