
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 an ellipse $C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($a > b > 0$), with the right focus $F_2$, the origin $O$, and a point $M$ on the y-axis. The point $A$ is an intersection point of the line $MF_2$ with the ellipse $C$, and it's given that $|OA|=|OF_2|=3|OM|$, find the eccentricity of the ellipse $C$.

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