
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 "nicely odd" number as an integer greater than 1 that equals the product of its distinct proper divisors, where all involved primes are odd. Among these numbers, some can be expressed as the product of two distinct odd prime numbers and others as the cube of an odd prime number. Find the sum of the first ten "nicely odd" numbers.

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