
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
Does there exist a mapping \( f: \mathbf{N} \rightarrow \mathbf{N} \) that satisfies
$$
f(f(n))=f(n)+n,
$$
with the conditions
$$
\begin{aligned}
f(1) & = 2 \\
f(n+1) & > f(n) ?
\end{aligned}
$$

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