
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 defined by $\frac{x^2}{p^2} + \frac{y^2}{q^2} = 1$. The point $B$ is located at $(0,q)$ and side $\overline{AC}$ is parallel to the x-axis. The foci of the ellipse, $F_1$ and $F_2$, lie on the y-axis and x-axis respectively. Given that $F_1 F_2 = 4$, find the ratio $\frac{AB}{F_1 F_2}$.

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