
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 $A$, $B$, $C$, $D$ are located on the circle defined by $x^{2}+y^{2}=16$. All of these points have integer coordinates. The distances $AB$ and $CD$ are both irrational numbers. What is the maximal possible value of the ratio $\frac{AB}{CD}$?
A) 1
B) 2
C) $\sqrt{2}$
D) $\sqrt{3}$
E) $\sqrt{5}$

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