
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
Ellipse $Γ:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$ has its left focus at $F$, right vertex at $A$. The line $l$ passing through point $F$ at an angle of $45^{\circ}$ intersects the ellipse $Γ$ at points $M$ and $N$ (point $M$ is above the $x$-axis). If triangle $AMF$ is a right isosceles triangle, determine the eccentricity of ellipse $Γ$.

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