
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
The function  $f: N \to N_0$  is  such that  $f (2) = 0, f (3)> 0, f (6042) = 2014$  and   $f (m + n)- f (m) - f (n) \in\{0,1\}$  for all  $m,n \in N$ . Determine  $f (2014)$ .   $N_0=\{0,1,2,...\}$ 

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