
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
Through the point $M(1,1)$, a line with slope $- \frac {1}{2}$ intersects an ellipse $C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 (a > b > 0)$ at points $A$ and $B$. If $M$ is the midpoint of line segment $AB$, then the eccentricity of the ellipse $C$ equals ____.

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