
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 (not necessarily different) positive integers not exceeding  $10$  is equal to  $S$ .
Find all possible values of  $S$  such that these numbers can always be partitioned into two groups with the sum of the numbers in each group not exceeding  $70$ .

*(I. Voronovich)*

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