
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 four numbers such that the sums of any three of them are 22, 24, 27, and 20. (This problem was given by the Greek mathematician Diophantus, who lived in the 2nd century AD).

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