
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
A set contains four numbers. The six pairwise sums of distinct elements of the set, in no particular order, are  $189$ ,  $320$ ,  $287$ ,  $234$ ,  $x$ , and  $y$ . Find the greatest possible value of  $x+y$ .

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