
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
It is known that the polar equation of the ellipse C is $\rho^2=\frac {12}{3\cos^{2}\theta+4\sin^{2}\theta}$. Points $F_{1}$ and $F_{2}$ are its left and right foci, respectively. Establish a Cartesian coordinate system with the pole as the origin and the polar axis as the positive half of the x-axis. The parametric equation for line l is $\begin{cases} x=2+\frac{\sqrt{2}}{2}t \\ y=\frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter, $t\in\mathbb{R}$).
1. Find the standard equation for line l and the Cartesian equation of the ellipse C.
2. Find the sum of distances from points $F_{1}$ and $F_{2}$ to the line l.

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