
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
Suppose that \(a\) and \(b\) are positive integers where \(a\) has \(3\) factors and \(b\) has \(a\) factors. Moreover, \(b\) is divisible by \(a\). What is the least possible value of \(b\) if \(a\) is the square of the next smallest prime greater than in the original problem?

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