
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 some numbers from \(1, 2, 3, \ldots, 9, 10\) so that each of the 20 numbers \(1, 2, 3, \ldots, 19, 20\) is equal to one of the selected numbers or the sum of two selected numbers (they can be the same). How many numbers need to be selected at least?

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