
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
Points $A$, $B$, $C$, $D$ are on the circle described by $x^2 + y^2 = 100$ and have integer coordinates. Distances $AB$ and $CD$ are irrational numbers. Determine the maximum possible value of the ratio $\frac{AB}{CD}$.
A) 6 
B) 7 
C) 4√2 
D) 8√2

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