
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
Define the adjusted proper divisor rule such that a number \( n \) is defined as "nice-plus" if \( n \) can either be expressed as the product of two or three distinct prime factors. Find the sum of the first ten "nice-plus" numbers.

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