
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
Given a polar coordinate system established in the Cartesian coordinate system xOy with the origin as the pole and the positive x-axis as the polar axis, the polar equation of the conic section C is $\rho^2 = \frac{12}{3+\sin^2\theta}$. F1 is the left focus of the conic section C. The line l is given by the parametric equations $x=-1+t$ and $y=\sqrt{3}t$ (where t is the parameter).

(I) Find the Cartesian equations for the conic section C and the line l.

(II) If the line l intersects the conic section C at points M and N, find the sum of the distances |F1M| + |F1N|.

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