
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
Petya invented four distinct natural numbers and wrote down all their pairwise sums on the board. Below those, he wrote all their sums taken three at a time. It turned out that the sum of the two largest pairwise sums and the two smallest sums from those taken three at a time (a total of four sums) is 2017. Find the largest possible value of the sum of the four numbers that Petya invented.

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