
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
On a board, there are written four non-zero numbers such that the sum of any three of them is less than the fourth number. What is the minimum number of negative numbers that can be written on the board? Justify your answer.

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