
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 is a set of 20 weights that can be used to weigh any whole number weight from 1 to 1997 grams (the weights are placed on one side of the scale, the weight being measured on the other). What is the minimum possible weight of the heaviest weight in such a set if:

a) the weights in the set are all whole numbers,

b) the weights are not necessarily whole numbers

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