
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 natural number greater than 1 will be called super-nice if it is equal to the product of its distinct proper divisors, where the number is either the product of a square of a prime and another distinct prime or the fourth power of a prime. What is the sum of the first ten super-nice numbers?

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