
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
Starting with a list of three numbers, the “*Make-My-Day*” procedure creates a new list by replacing each number by the sum of the other two. For example, from  $\{1, 3, 8\}$  “*Make-My-Day*” gives  $\{11, 9, 4\}$  and a new “*MakeMy-Day*” leads to  $\{13, 15, 20\}$ . If we begin with  $\{20, 1, 8\}$ , what is the maximum difference between two numbers on the list after  $2018$  consecutive “*Make-My-Day*”s?

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