
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
If we write the progression $\div 4, 8, (16, 32), \ldots, \left(2^{2n}, 2^{2n+1}\right)$, then every pair of numbers in brackets gives a perfect number if we multiply the larger number in the pair, decreased by one, by the smaller number.

Note: Provided that $2^{2n+1} - 1$ is a prime number.

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