
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 $g(n)$ return the number of distinct ordered triples of positive integers $(a, b, c)$ such that $a^2 + b^2 + c^2 = n$. Note that all triples where any two or three coordinates differ are considered distinct. What is the smallest positive integer $n$ for which $g(n) = 3$?

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