
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
There are 100 weights of different masses on a table. A weight is called "lucky" if its mass is equal to the sum of the masses of some two other weights on the table. What is the minimum number of lucky weights that guarantees that the masses of some two weights differ by at least three times?

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