
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 came up with four distinct natural numbers and wrote down all their pairwise sums on the board, and below that, wrote down all their sums taken three at a time. It turned out that the sum of the two largest numbers from the top row and the two smallest numbers from the bottom row (a total of four numbers) is 2017. Find the maximum possible value of the sum of the four numbers that Petya came up with.

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