
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 0 is called a perfect number if the sum of all its factors equals twice the number itself. For example, the factors of 6 are \(1, 2, 3, 6\), and \(1 + 2 + 3 + 6 = 12\). Therefore, 6 is the smallest perfect number. The question of whether there are infinitely many perfect numbers remains an open problem in mathematics. To study perfect numbers, we can start by calculating the sum of all factors of a natural number. The sum of all factors of 8128 is \(\qquad\).

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