
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
$$
\min_{k \in \mathbb{N}} \left( k^2 + \left\lfloor \frac{n}{k^2} \right\rfloor \right) = 1991
$$
where \( \left\lfloor \frac{n}{k^2} \right\rfloor \) denotes the greatest integer less than or equal to \( \frac{n}{k^2} \), and \(\mathbb{N}\) is the set of natural numbers.

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