
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 the 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 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 $\lambda_1 + \lambda_2$ when m varies.

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