
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
A positive integer is called "primer" if it has a prime number of distinct prime factors. A positive integer is called "primest" if it has a primer number of distinct primer factors. A positive integer is called "prime-minister" if it has a primest number of distinct primest factors. Let \( N \) be the smallest prime-minister number. Estimate \( N \). 

An estimate of \( E > 0 \) earns \( \left\lfloor 20 \min \left(\frac{N}{E}, \frac{E}{N}\right) \right\rfloor \) points.

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