
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 a 'nice' number as a natural number greater than 1 that equals the product of its distinct proper divisors. A natural number can be considered nice if it meets one of the following conditions:
1. It is a product of two distinct primes.
2. It is a cube of a prime.
3. It is a product of the square of a prime and another distinct prime. 
Find the sum of the first ten 'nice' numbers considering the above conditions.

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