
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 defined as "lovely" if it is equal to the sum of its distinct proper divisors squared. Determine the sum of the first five lovely numbers.

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