
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 that  $A,B,$  and  $C$  are noncollinear points in the plane with integer coordinates such that the distances  $AB,AC,$  and  $BC$  are integers, what is the smallest possible value of  $AB?$ 

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