
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
The sum of several positive integers, not necessarily different, all of them less than or equal to  $10$ , is equal to  $S$ . We want to distribute all these numbers into two groups such that the sum of the numbers in each group is less than or equal to  $80.$  Determine all values ​​of  $S$  for which this is possible.

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