
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
The product of two natural numbers \(a\) and \(b\) is a three-digit number that is the cube of some natural number \(k\). The quotient of the numbers \(a\) and \(b\) is the square of that same number \(k\). Find \(a\), \(b\), and \(k\).

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