
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  $\displaystyle f : \mathbb N^\ast \to \mathbb N^\ast$  ( $\displaystyle N^\ast = \{ 1,2,3,\ldots \}$ ) with the property that, for all  $\displaystyle n \geq 1$ , \[ f(1) + f(2) + \ldots + f(n)  \] is a perfect cube  $\leq n^3$ .

*Dinu Teodorescu*

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