
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 whose sum of all proper divisors (divisors excluding the number itself) equals the number itself is called a perfect number (also known as a complete number), such as $6=1+2+3$; $28=1+2+4+7+14$; $496=1+2+4+8+16+31+62+124+248$. Moreover, they can all be represented as the sum of some consecutive positive integer powers of $2$, such as $6={{2}^{1}}+{{2}^{2}}$, $28={{2}^{2}}+{{2}^{3}}+{{2}^{4}}$, $\cdots$, following this pattern, $8128$ can be represented as \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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