
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
The function $g$ maps nonnegative integers to real numbers, defined with $g(1) = 1$ and
\[ g(m^2 + n^2) + g(m^2 - n^2) = g(2m^2) + g(2n^2) \]
for all nonnegative integers $m$ and $n$, where $m^2 \ge n^2$. Determine all possible values of $g(10)$.

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