
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 line $$L:x=my+1$$ passes through the right focus F of the ellipse $$C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ and intersects the ellipse C at points A and B.  
(1) If the focus of the parabola $$x^{2}=4 \sqrt {3}y$$ is the top vertex of the ellipse C, find the equation of the ellipse C;  
(2) For the ellipse C in (1), if the line L intersects the y-axis at point M, and $$\overrightarrow {MA}=\lambda _{1} \overrightarrow {AF}, \overrightarrow {MB}=\lambda _{2} \overrightarrow {BF}$$, find the value of $\lambda_1+\lambda_2$ as m varies.

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