
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
Suppose \(ABC\) is a triangle with circumcenter \(O\) and orthocenter \(H\) such that \(A\), \(B\), \(C\), \(O\), and \(H\) are all on distinct points with integer coordinates. What is the second smallest possible value of the circumradius of \(ABC\)?

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