
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
Distinct points \(A\), \(B\), \(C\), \(D\) lie on the circle \(x^2 + y^2 = 16\) and have integer coordinates. The distances \(AB\) and \(CD\) are irrational numbers. What is the greatest possible value of the ratio \(\frac{AB}{CD}\)?
A) \(\sqrt{2}\)
B) 2
C) \(\sqrt{5}\)
D) 3
E) \(\sqrt{8}\)

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