
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 that the line $l$ intersects the ellipse $\frac{x^2}{6}+\frac{y^2}{3}=1$ in the first quadrant at points $A$ and $B$, and intersects the $x$-axis and $y$-axis at points $M$ and $N$ respectively, with $|MA|=|NB|$ and $|MN|=2\sqrt{3}$, find the equation of line $l$.

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