
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
Determine all functions  $f:\mathbb{Z}^+\to \mathbb{Z}$  which satisfy the following condition for all pairs  $(x,y)$  of *relatively prime* positive integers:
\[f(x+y) = f(x+1) + f(y+1).\]

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