
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 the function $g$ take nonnegative integers to real numbers, defined by $g(1) = 2$, and
\[g(m + n) + g(m - n) = 2[g(m) + g(n)]\]
for all nonnegative integers $m \ge n$. Find the value of $g(10)$.

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