
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 four weights and a two-pan balance scale without an indicator. How many different weights can be exactly measured with these weights, if

a) the weights can only be placed on one pan of the scale;

b) the weights can be placed on both pans of the scale.

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