
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 satisfies two conditions:
1. It is equal to the product of its distinct proper divisors.
2. It is also equal to the sum of its distinct proper divisors.
What is the sum of the first five "super nice" numbers?

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