
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 function \( f \) from the positive integers to the positive integers such that \( f(1) = 2 \), \( f(f(n)) = f(n) + n \) for all \( n \), and \( f(n) < f(n+1) \) for all \( n \)?

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