
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
A circle with radius 5 units has an equilateral triangle ABC inscribed in it, such that point B is at the top of the circle (0,5). Sides AC and AB are symmetric with respect to the y-axis, and the x-coordinates of points A and C are equal but opposite. If points F1 and F2 are the midpoints of sides AB and BC, respectively, find the ratio of the length of side AB to the distance between F1 and F2.

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