
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 left and right foci $F_{1}$ and $F_{2}$, respectively. There exists a point $M$ in the first quadrant of ellipse $C$ such that $|MF_{1}|=|F_{1}F_{2}|$. The line $F_{1}M$ intersects the $y$-axis at point $A$, and $F_{2}A$ bisects the angle $\angle MF_{2}F_{1}$. Find the eccentricity of the ellipse $C$.

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