
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
In a set of weights, all of which have different masses, it is known that if any pair of weights is placed on the left pan, the balance can be achieved by placing one or more of the remaining weights on the right pan. Find the smallest possible number of weights in the set.

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