
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
We have a two-pan balance and want to be able to weigh any object with an integer mass between 1 and 40 kg. What is the minimum number of weights with integer masses needed to achieve this:

1. if the weights can only be placed on one pan of the balance?
2. if the weights can be placed on both pans of the balance?

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