
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 $C$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$, the focus of the parabola $x^{2}=4\sqrt{3}y$ is the upper vertex of the ellipse $C$, and the line $l$ intersects the ellipse $C$ at points $A$ and $B$.

1. Find the equation of the ellipse $C$.
2. If the line $l$ intersects the $y$-axis at point $M$, and $\overrightarrow{MA}=\lambda_{1}\overrightarrow{AF}, \overrightarrow{MB}=\lambda_{2}\overrightarrow{BF}$, is the value of $\lambda_{1}+\lambda_{2}$ a constant as $m$ varies? If so, find this constant. If not, explain why.

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