
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
Given some positive integers not exceeding 10 (they can be the same) whose sum is $S$. Find all possible values of $S$ such that these numbers can be divided into two parts, each with a sum not exceeding 80.

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