
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
Noémie and Tristan are shepherds, each owning a number of sheep that is a perfect square. Let $a^2$ represent the number of Noémie’s sheep and $b^2$ represent the number of Tristan’s sheep. It is known that $97 \leqslant a^2 + b^2 \leqslant 108$. Determine the number of sheep each one owns given the following conditions:

1. Noémie has strictly more sheep than Tristan;
2. Each has at least 2 sheep;
3. The total number of sheep $a^2 + b^2$ is odd.

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