
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
The parametric equation of line $l$ is given by $$\begin{cases} x=1+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}(t\text{ is the parameter})$$, and the polar equation of curve $C$ is $(1+\sin^2{\theta})\rho^2=2$.
1. Write the Cartesian equation of line $l$ and curve $C$.
2. Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and there is a point $P(2, \sqrt{3})$. Find the value of $|PA|+|PB|$.

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