
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 five numbers. The ten pairwise sums of distinct elements of the set, in no particular order, are $210$, $340$, $290$, $250$, $370$, $x$, $y$, $z$, $w$, and $u$. Find the greatest possible value of $x+y+z+w+u$.

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