
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
Alice writes differents real numbers in the board, if  $a,b,c$  are three numbers in this board, least one of this numbers  $a + b, b + c, a + c$  also is a number in the board. What's the largest quantity of numbers written in the board???

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