
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 regarded as "grand" if it is equal to the product of all its distinct proper divisors. Define a grand number in two cases:
1. It is the product of a square of a prime and a different distinct prime.
2. It is the cube of a prime number.
What is the sum of the first ten grand numbers?

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