
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
Given the following groups of pairs of positive integers: the 1st group is {(1,2), (2,1)}, the 2nd group is {(1,3), (3,1)}, the 3rd group is {(1,4), (2,3), (3,2), (4,1)}, the 4th group is {(1,5), (2,4), (4,2), (5,1)}, ..., determine the 21st pair in the 40th group.

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