
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]


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Define a function $f$ from nonnegative integers to real numbers, with $f(1) = 1$ and the functional equation:
\[ f(m+n) + f(m-n) = 3(f(m) + f(n)) \]
for all nonnegative integers $m \ge n$. Determine $f(10)$.

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