
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
Determine all functions  $f: \mathbb{Z}\to\mathbb{Z}$  satisfying \[f\big(f(m)+n\big)+f(m)=f(n)+f(3m)+2014\] for all integers  $m$  and  $n$ .

*Proposed by Netherlands*

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