
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 circle defined by $x^2 + y^2 = 16$ where points $A$, $B$, $C$, $D$ have integer coordinates and lie on the circle. The distances $AB$ and $CD$ are irrational. What is the greatest possible value of the ratio $\frac{AB}{CD}$?
A) $2\sqrt{2}$
B) 4
C) $\sqrt{2}$
D) $2\sqrt{3}$
E) 3

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