
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]


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Given an ellipse $\frac{{{x^2}}}{{{a^2}}}+\frac{{{y^2}}}{{{b^2}}}=1({a＞b＞0})$ with left and right foci $F_{1}$ and $F_{2}$ respectively, find the eccentricity of the ellipse, given that point $A$ is an endpoint of the minor axis and $\cos \angle F_{1}AF_{2} = \frac{5}{6}$.

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