
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 is termed excellent if it is equal to the product of its distinct proper divisors. Determine the sum of the first ten excellent numbers, where a number is excellent if it is either formed by the product of two distinct prime numbers each raised to the power of 2, or if it is the fourth power of a prime number.

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