
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 positive integer is called a perfect number (also known as a complete number or a friendly number) if the sum of all its proper divisors (positive divisors excluding the number itself) equals the number itself. For example, $6=1+2+3$; $28=1+2+4+7+14$; $496=1+2+4+8+16+31+62+124+248$. Moreover, these perfect numbers can be represented as the sum of consecutive positive integral powers of $2$, such as $6=2^{1}+2^{2}$, $28=2^{2}+2^{3}+2^{4}$, etc. Following this pattern, $8128$ can be represented as \_\_\_\_\_\_.

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