
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 $g$ be a function taking the nonnegative integers to the nonnegative integers, such that
\[2g(a^2 + b^2 + 1) = [g(a)]^2 + [g(b)]^2\] for all nonnegative integers $a$ and $b.$

Let $n$ be the number of possible values of $g(26),$ and let $s$ be the sum of the possible values of $g(26).$ Find $n \times s.$

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