
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 two foci of the ellipse $C$ are $F\_1$ and $F\_2$, a line passing through point $F\_1$ intersects the ellipse $C$ at points $M$ and $N$. If $|MF\_2|=|F\_1F\_2|$, and $|MF\_1|=2$, $|NF\_1|=1$, determine the eccentricity of the ellipse $C$.

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