
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
Select several numbers from $1, 2, 3, \cdots, 9, 10$ so that every number among $1, 2, 3, \cdots, 19, 20$ can be expressed as either one of the selected numbers or the sum of two selected numbers (which can be the same). What is the minimum number of selections needed?

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