
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]


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A natural number greater than 1 is called "enhanced nice" if it is equal to the product of its distinct proper divisors or to the product of its prime factors each raised to a power less than its exponent in the factorization. Determine the sum of the first ten "enhanced nice" numbers under this new definition.

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