
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
Find all functions \( f: \mathbf{Z}^{+} \rightarrow \mathbf{R} \) that satisfy the identity

\[ 
f(n+m)+f(n-m) \equiv f(3n), \quad n, m \in \mathbf{Z}^{+}, \quad n \geqslant m 
\]

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