
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
The buyer is allowed only one type of weighing: to place one of the diamonds on one scale pan, weights on the other, and verify that the mass on the corresponding label is correct. However, for each weight taken, the buyer has to pay the seller 100 coins. If a weight is removed from the scale and does not participate in the next weighing, the seller takes it back. What is the minimum amount that needs to be paid to verify the masses of all the diamonds?

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