
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 \( f: \mathbf{Z} \rightarrow \mathbf{Z} \) such that for all integers \( m \) and \( n \), the following equation holds:
\[
f(f(m) + n) + f(m) = f(n) + f(3m) + 2014
\]

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