
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 \(1, 2, 3, \cdots, 9, 10\) such that each number from \(1, 2, 3, \cdots, 19, 20\) is equal to the sum of one or two of the selected numbers (they can be the same). Find the minimum number of selected numbers needed.

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