
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 injective functions  $f: \mathbb R \rightarrow \mathbb R$  such that for every real number  $x$  and every positive integer  $n$ ,  $$  \left|\sum_{i=1}^n i\left(f(x+i+1)-f(f(x+i))\right)\right|<2016 $$  *(Macedonia)*

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