
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
Find all pairs of natural numbers  $(\alpha,\beta)$  for which, if  $\delta$  is the greatest common divisor of  $\alpha,\beta$ , and  $\varDelta$  is the least common multiple of  $\alpha,\beta$ , then 
\[ \delta + \Delta = 4(\alpha + \beta) + 2021\]


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