
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
Ivan Karlovich Buratino, being in financial difficulty, turned to the famous criminal authority Basilio, nicknamed "the Cat," for financial help. The Cat offered Buratino a loan of 100 coins for a term of 128 days with two alternative conditions.

Option 1: An interest rate of 1% on the current debt amount per day, with daily compounding interest.

Option 2: An interest rate of 2% per day on the initial debt amount.

Buratino chose the first option.

How many coins did he overpay/save compared to the second option?

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