
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 functions  $ f: \mathbb{N} \to \mathbb{Z} $  satisfying   $$  n \mid f\left(m\right) \Longleftrightarrow m \mid \sum\limits_{d \mid n}{f\left(d\right)}  $$   holds for all positive integers  $ m,n $ 

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