
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
The line $x - \sqrt{3}y + \sqrt{3} = 0$ intersects the ellipse $\frac{x^2}{9} + \frac{y^2}{6} = 1$ at points M and N. If O is the origin, find the area of triangle OMN.

A) $\sqrt{3}$
B) $\frac{2\sqrt{3}}{3}$
C) $\frac{3\sqrt{3}}{2}$
D) $\frac{4\sqrt{3}}{3}$

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