
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 all \( x \in \mathbb{R} \) and \( n \in \mathbb{N} \):

\[ 
\left|\sum_{i=1}^{n} i(f(x+i+1)-f(f(x+i)))\right| \leq 2019 
\]

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