
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
An equilateral triangle $ABC$ is inscribed in the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$, such that $B$ is at $(0, 2)$ and $\overline{AC}$ is parallel to the x-axis. Foci $F_1$ and $F_2$ lie on sides $\overline{BC}$ and $\overline{AB}$ respectively, as shown below. Find $\frac{AB}{F_1F_2}$.

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