
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 \(210\), \(335\), \(296\), \(245\), \(x\), and \(y\). None of the pairwise sums are repeated, and all are distinct. Find the greatest possible value of \(x + y\).

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