
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
Let \( F_{1} \) and \( F_{2} \) be the two foci of an ellipse. A circle with center \( F_{2} \) is drawn, which passes through the center of the ellipse and intersects the ellipse at point \( M \). If the line \( ME_{1} \) is tangent to circle \( F_{2} \) at point \( M \), find the eccentricity \( e \) of the ellipse.

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