
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
Kim borrows $100$ dollars from Sam with a simple interest rate of $10\%$ per day. Additionally, there's a one-time borrowing fee of $10$ dollars that is added to the debt immediately. What is the least integer number of days after which Kim will owe Sam at least twice as much as she borrowed?

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