
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 $F_1$ and $F_2$ are the two foci of an ellipse, a circle with center $F_2$, denoted as circle $F_2$, passes through the center of the ellipse and intersects the ellipse at point $M$. If the line $MF_1$ is tangent to circle $F_2$, calculate the eccentricity $e$ of the ellipse.

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