
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 $n$ different positive numbers. Sums are formed from them with any number of addends from 1 to $n$.

a) What is the smallest number of different sums that can be obtained?

b) What is the largest number of different sums that can be obtained?

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