
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 the equation of an ellipse \\( \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a > b > 0)\\), \\(F\_{1}\\) and \\(F\_{2}\\) are its left and right foci respectively, \\(O\\) is the coordinate origin, \\(A\\) is any point on the ellipse other than the vertex, \\(∠AF\_{1}F\_{2}=30^{0}, AO=OF\_{2}\\), the eccentricity of the ellipse \\(e=\\) \_\_\_\_\_\_ .

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