
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 natural numbers \( n \) such that
$$
\min_{k \in \mathbf{N}}\left(k^{2}+\left\lfloor \frac{n}{k^{2}} \right\rfloor \right) = 1991 \quad (n \in \mathbf{N}).
$$

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