
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
Define the function $g$ mapping nonnegative integers to real numbers, such that $g(2) = 4$, and
\[ g(m+n) + g(m-n) = \frac{3g(2m) + g(2n)}{4} \]
for all nonnegative integers $m \ge n$. Find the sum of all possible values of $g(10)$.

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