
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
Let  $A, B, C, D$  be four distinct points in the plane such that the length of the six line segments  $AB, AC, AD, BC, BD, CD$  form a  $2$ -element set  ${a, b}$ . If  $a > b$ , determine all the possible values of  $\frac ab$ .

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