
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 the center of a hyperbola is at the origin of the coordinate, if the left focus $F$ and the right vertex $A$, as well as the vertex $B$ on the imaginary axis form a right-angled triangle, then its eccentricity is $\frac{\sqrt{5}+1}{2}$, which is called the "Golden Hyperbola". By analogy with the "Golden Hyperbola", the eccentricity of the "Golden Ellipse" can be deduced as $\_\_\_\_\_\_$.

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